Intelligent Prediction of Stuck Pipe Using Combined Data-Driven and Knowledge-Driven Model
Intelligent Prediction of Stuck Pipe Using Combined Data-Driven and Knowledge-Driven Model
Zhu, Shuo;Song, Xianzhi;Zhu, Zhaopeng;Yao, Xuezhe;Liu, Muchen
2022-05-23 00:00:00
applied sciences Article Intelligent Prediction of Stuck Pipe Using Combined Data-Driven and Knowledge-Driven Model 1 2 , 3 , 2 2 2 Shuo Zhu , Xianzhi Song *, Zhaopeng Zhu , Xuezhe Yao and Muchen Liu Jianghan Machinery Research Institute Limited Company of CNPC, Wuhan 430000, China; 2019211810@student.cup.edu.cn School of Petroleum Engineering, China University of Petroleum, Beijing 102249, China; zhuzp@cup.edu.cn (Z.Z.); 2019211811@student.cup.edu.cn (X.Y.); 2018010309@student.cup.edu.cn (M.L.) State Key Laboratory of Petroleum Resources and Prospecting, Beijing 102249, China * Correspondence: songxz@cup.edu.cn; Tel.: +86-010-8973-2176 Abstract: Stuck pipe phenomena can have disastrous effects on drilling performance, with outcomes that can range from time delays to loss of expensive machinery. In this work, we provide three methods for the prediction of stuck pipe. The first method targets the detection of friction coefficient which can represent the trend of stuck pipe. The second method targets the prediction of probability for stuck pipe using ANN (artificial neural network). The last model establishes a comprehensive indicator based on the first and the second method using fuzzy mathematics which can give more accurate probability for stuck pipe. The results show that the best model is the last one which can predict stuck pipe events with a F1 of 0.98 and a FAR (false alarm rate) of 1%. Preliminary experimental results on the available dataset indicate that the use of the proposed model and can help mitigate the stuck pipe issue. Keywords: stuck pipe; drag coefficient; neural network; fuzzy mathematics Citation: Zhu, S.; Song, X.; Zhu, Z.; Yao, X.; Liu, M. Intelligent Prediction of Stuck Pipe Using Combined 1. Introduction Data-Driven and Knowledge-Driven Drilling is a key process to oil and gas exploration and development which is full Model. Appl. Sci. 2022, 12, 5282. of randomness, uncertainty and concealment. It is necessary to place several thousand https://doi.org/10.3390/app meters of drill pipe in a narrow space with a diameter of only 200–500 mm. Unreasonable design of engineering parameters and unclear understanding of the formation often lead to Academic Editor: José A.F.O. Correia complex downhole accidents (lost circulation, well collapse, stuck pipe, etc.), among which stuck pipe is one of the most common accidents. Received: 27 April 2022 According to the statistics of complex accidents in the South China Sea during Accepted: 16 May 2022 2009–2018, about 45% of them were stuck pipe [1]. Mudlog data from Tarim Oilfield Published: 23 May 2022 in China shows that it takes about 3 months to deal with a serious stuck pipe accident Publisher’s Note: MDPI stays neutral which increases non-productive times and seriously affects drilling efficiency. Therefore, with regard to jurisdictional claims in the timely prediction of stuck pipe events is considered a primary necessity to assist the published maps and institutional affil- drilling team in the decision-making process, so that appropriate countermeasures can be iations. put in effect before the situation slips out of hand. Mudlog data shows that the stuck pipe accidents occur in the process of tripping and drilling with varying degrees of severity. For example, in some highly deviated wells and horizontal wells, the stuck pipe accident is often accompanied in the process of tripping, Copyright: © 2022 by the authors. but it is usually not serious. On the contrary, more attention is paid to the stuck pipe during Licensee MDPI, Basel, Switzerland. drilling. Once the drill string is completely stuck, it can only be lifted by explosion and a This article is an open access article new side drilling scheme need to be redesigned, which seriously restricts the safety and distributed under the terms and efficiency of drilling. Therefore, we focus on the real-time prediction of stuck pipe in the conditions of the Creative Commons process of drilling. Attribution (CC BY) license (https:// creativecommons.org/licenses/by/ 4.0/). Appl. Sci. 2022, 12, 5282. https://doi.org/10.3390/app12105282 https://www.mdpi.com/journal/applsci Appl. Sci. 2022, 12, 5282 2 of 16 Many approaches have been developed to predict and reduce the risk of stuck pipe. In summary, the analysis and prediction of stuck pipe accidents can be divided into two parts: data-driven and knowledge-driven. For the knowledge-driven model, cuttings, wellbore tortuosity and other factors will eventually lead to the increase of torque and drag which can lead to the occurrence of stuck pipe accident. Therefore, researchers use the torque and drag model to invert the friction coefficient to realize the qualitative analysis of stuck pipe trend in the view of mechanics. However, this method is mainly used to analyze and deal with the stuck pipe after drilling considering that the WOB (weight on bit) and TOB (torque on bit) cannot be transmitted in real time. For the data-driven model, researchers applied support vector machine, random forest, neural network and other algorithms to the prediction of stuck pipe. However, the generalization ability and reliability of the intelligent model need to be further improved due to the quantity and quality of samples and the differences between blocks. Based on previous research, we establish a comprehensive indicators based on the knowledge-driven and data-driven model using fuzzy mathematics, which is expected to realize accurate prediction of stuck pipe and ensure the safety and efficiency of drilling The remaining of this paper is organized as follows: Section 2 discusses the literature review of the prediction methods of stuck pipe. Section 3 introduces our proposed method. Section 4 explains the experimental results and discusses the main findings and finally Section 5 concludes this research and provides some plans for future work. 2. Related Research This section introduces the related research on the analysis and prediction of stuck pipe, including knowledge-driven and data-driven model. For the knowledge-driven model, in [2], the paper shows how to estimate two friction coefficients on a foot-by-foot basis at the wellsite with both measurement-while-drilling (MWD) and surface values of weight on bit (WOB) and torque. A log of the coefficients with depth can be used to diagnose drilling problems in directional wells. Field examples are given that show how the technique detects incipient stuck pipe. Since downhole data cannot be transmitted in real time, this method is mainly used after drilling. In [3], they present the results of the application of torque and drag model to directional wells drilled worldwide which was effectively used in these cases to aid in planning the directional program before spudding, to monitor the wells during drilling, and to analyze particular drilling problems after completion. In [4], the paper describes investigation of the friction between the pipe and the mud cake. It was found that the apparent coefficient of friction, or the “stuck pipe” coefficient, was not a constant; instead, it increased with increased time of contact between plate and mud cake. They think that the friction factor and mud cake quality are the factors that cannot be ignored. In [5], mud logging and daily reports of 75 wells in one of Iranian Southwest oil fields were studied. Mud weight, yield point, plastic viscosity and so on, a total of seven parameters were employed to introduce a new parameter called Reducing Stuck Index (RSI). For this field, the comparison of RSI of the current well with those of drilled wells predicted the probability of occurrence of stuck pipe very well. In [6], Dunbar conducted a theoretical study on the bit stuck pipe caused by borehole deformation. It is found that this phenomenon is related largely to the magnitude of the lateral earth stresses, formation mechanical properties, and drilling-tool geometry. For the data-driven models, Kingsborough [7] used the multivariate discriminant analysis method to study stuck pipe for the first time. This method can be used to distin- guish mechanical stuck, differential pressure stuck and non-stuck. Murillol [8] introduced mathematical methods such as fuzzy comprehensive discrimination and neural networks to predict stuck pipe, and proposed new methods for early warning and risk assessment of stuck pipe. Multivariate statistical regression and a discrimination analysis were developed for an Iranian field and presented by Shoraka [9] to predict and reduce the risks of stuck Appl. Sci. 2022, 12, 5282 3 of 16 pipe. Biegler and Kuhn [10] used multivariate analysis to quantify the impact of design variables on the overall stuck pipe. Artificial Neural Network (ANN) has been extensively used in literature to solve stuck pipe related issues. Some studies used ANN to predict a stuck pipe [11–13], using different input parameters and data sizes, which were collected from several fields. They concluded that ANN was capable of predicting stuck pipe events with varying model accuracy. In [13], Siruvuri suggested coupling the ANN model output with a drilling log viewer for monitoring. In [14], Elahi Naraghi applied several methods including ANN to predict stuck pipe events. Their study showed that both ANN and adaptive neuro-fuzzy inference systems are capable of predicting stuck pipe events with the same accuracy and suggested using ANN for simplicity. In [15], Albaiyat used ANN along with the support vector machine to predict stuck pipe events. In [16], Fuzzy logic and active learning were used for stuck pipe prediction. In [17], Automated real-time modeling and data analysis used to predict the risk of stuck pipe events were addressed by Salminen. In [18], Shahbazi and Shahri developed a stuck pipe risk analysis prediction model by introducing a stuck pipe index parameter. In [19], Zhigang Shan divided the drilling conditions into three situations and use ANN to realize the prediction of stuck-pipe. In [20], Runqiao Yu selected nine parameters and used the method of system dynamic cluster analysis to divide the stuck pipe accidents into three categories: mechanical stuck pipe, differential pressure stuck pipe and circulation stuck pipe. In [21], Jianming Liu have obtained the downhole engineering parameters according to the downhole measuring tools and established an intelligent model using stochastic forest algorithm. In [22], Brankovic have developed three indicators based on mudlog data, which aim to detect three different physical phenomena associated with the insurgence of stuck pipe. A statistical model that relates these features to documented stuck-pipe events was then developed using advanced machine learning tools. Through the analysis of the above related research, it is found that the stuck pipe analysis method based on knowledge-driven model is mainly used for monitoring and qualitative analysis of stuck pipe, but it is difficult to achieve prediction and quantitative analysis. Meanwhile, the accuracy and reliability of data-driven stuck pipe analysis method need to be further improved due to the number and quality of stuck pipe samples. Therefore, on the basis of previous studies, we put forward a comprehensive evalu- ation method which combines the knowledge-driven model with the data-driven model through fuzzy mathematics theory. 3. Proposed Methodology We provide three methods for the prediction of stuck pipe. The first method targets the detection of friction coefficient which can represent the trend of stuck pipe. The second method targets the prediction of probability for stuck pipe using ANN. The last model establishes a comprehensive indicator based on the first and the second method using fuzzy mathematics. Finally, we compare these three methods with the data from a well in Tarim Oilfield, China. 3.1. Real-Time Analysis of Stuck Pipe Trend Based on Inversion of Friction Coefficient The friction coefficient during drilling is a comprehensive resistance coefficient, which includes not only the friction between string and wellbore, but also the additional resistance caused by keyway, cuttings bed, mud viscous resistance and other factors. These factors are closely related to stuck pipe phenomenon, so the friction coefficient of string can characterize the stuck condition to a certain extent. Four basic parameters are needed to realize the real-time inversion of friction coeffi- cient, including hook tension, torque, WOB and TOB. The hook tension and torque can be measured in real time. WOB and TOB can be measured by downhole measurement tools which is usually stored in downhole tools and read after tripping out. So it is difficult to realize the real-time transmission of WOB and TOB under the existing technical conditions, which leads to the failure of real-time inversion of friction coefficient during drilling. There- Appl. Sci. 2022, 12, 5282 4 of 16 fore, the neural network technology is used to realize the real-time calculation of WOB and TOB [23]. 3.1.1. Real-Time Intelligent Calculation of WOB and TOB Mudlog Data Preprocessing 1 Feature selection The WOB and TOB are related to many factors during drilling. Through the analysis of physical problems, the following parameters are selected as input parameters. Among them, the time sequence parameters are: WOB, TOB, depth, inclination, azimuth, torque, rpm, stand pipe pressure, outlet flow, inlet density, outlet density, total pool volume, hook tension, mud density, mud viscosity, mud plastic viscosity. Non-sequential parameters include: mud system, BHA (bottom hole assembly) and bit type. 2 Normalization For sequential parameters, considering that mudlog parameters rarely have extreme maximum and minimum values and are restricted by drilling equipment capabilities, the maximum and minimum parameters can be set in advance or obtained by statistical analysis, so the minimax normalization method is used to normalize the time series data. For non-sequential parameters, the mud system is divided into water-based, oil-based and gas-based; Bit types are divided into PDC and cone; BHA is divided into pendulum, eyeful and tower. The above parameters are digitized by one hot method. Neural Network Optimization and Structure Design According to the characteristics of mudlog data in sequence and non-sequence, the adaptive neural networks, namely BP [24] and LSTM [25] networks, are selected. The formula of BP neural network is as follows, h = f (w x + b ) (1) t h t h x is the current input; w is the weight matrix of hidden layer; b is the offset vector of the t h h hidden layer; f is the activation function; h is the current output. The BP neural network with the unidirectional communication is a static network. Although it can approximate arbitrarily complex functions, it cannot infer the subsequent information based on the previous information which does not have the memory ability. LSTM network with self-feedback can transfer the information of hidden layer neurons to the next hidden layer neurons. It has certain memory ability and obvious advantages in dealing with sequential problems. The formula of LSTM neural network is as follows. Forget gate: f = s(W [h , x ] + b ) (2) t t f t 1 f Input gate: i = s(W [h , x ] + b ) (3) t i t 1 t i Output gate: O = s W h , x + b (4) ( [ ] ) t o t 1 t o x is the current input; h is the output at the previous moment; W is the weight matrix t t 1 f of the forget gate neuron in LSTM; b is the bias vector of the forget gate neuron in LSTM; f is the forget gate neuron in LSTM The output of the cell; W is the weight matrix of the t i input gate neuron in LSTM; b is the bias vector of the input gate neuron in LSTM; i is the output of the input gate neuron in LSTM; W is the weight of the output gate neuron in LSTM Matrix; b is the bias vector of the output gate neuron in LSTM; O is the output of o t the output gate neuron in LSTM; s is the sigmoid activation function. Appl. Sci. 2022, 12, x FOR PEER REVIEW 5 of 16 input gate neuron in LSTM; bi is the bias vector of the input gate neuron in LSTM; it is the output of the input gate neuron in LSTM; Wo is the weight of the output gate neuron in LSTM Matrix; bo is the bias vector of the output gate neuron in LSTM; Ot is the output of Appl. Sci. 2022, 12, 5282 5 of 16 the output gate neuron in LSTM; 𝜎 is the sigmoid activation function. The BP neural network in Figure 1 is used to input non-sequential data which are digitized by one-hot and have a dimension of 8. An input sample of the BP network is a The BP neural network in Figure 1 is used to input non-sequential data which are digitized by one-hot and have a dimension of 8. An input sample of the BP network is a one-dimensional vector. one-dimensional vector. Figure 1. BP-LSTM dual input network structure. Figure 1. BP-LSTM dual input network structure. The LSTM network in Figure 1 is used to input sequential data. The historical time step isThe selected LSTM as 5, nand etwo a data rk in sample Figure input 1 is to u the sed LSTM to in network put seq isuenti a 5 a 16 l d matrix. ata. The historical time step is selected as 5, and a data sample input to the LSTM network is a 5 × 16 matrix. Training, Testing and Optimization of BP-LSTM The data from 74 wells in the same block of Tarim Oilfield is used to test and optimize Training, Testing and Optimization of BP-LSTM the BP-LSTM model. The data of 52 wells are used for training and the rest for testing. The number of network layers, the number of neurons, dropout and activation function The data from 74 wells in the same block of Tarim Oilfield is used to test and optimize are optimized and each model is trained 120 epochs. The three indexes of MAPE (mean the BP-LSTM model. The data of 52 wells are used for training and the rest for testing. absolute percentage error), RMSE (root mean square error) and model complexity which The number of network layers, the number of neurons, dropout and activation func- is the number of parameters to be trained are combined to optimize the model. The tion are optimized and each model is trained 120 epochs. The three indexes of MAPE experimental scheme of the BP-LSTM model is shown in Table 1. (mean absolute percentage error), RMSE (root mean square error) and model complexity N 2 which is the number of parameters to be trained are combined to optimize the model. The RMSE = y y (5) pre true i=1 experimental scheme of the BP-LSTM model is shown in Table 1. y y N pre true i=1 true MAPE = 1 N (6) (5) RMSE=−yy ( ) pre true i=1 y is the measured value; y is the predicted value; N is the number of samples. true pre Table 1. Test table of BP-LSTM network model. yy − pre true i=1 (6) WOB (kN) TOB (kNm) true Layers Neurons Layers Neurons Activation MAPE= Dropout RMSE MAPE RMSE MAPE (BP) (BP) (LSTM) (LSTM) Function (kN) (%) (kNm) (%) 1 1 32 1 16 0.1 sigmoid 77.3 39.5 6.2 29.0 ytrue is the measured value; ypre is the predicted value; N is the number of samples. 2 1 64 1 32 0.3 tanh 23.8 13.0 2.8 12.8 3 1 128 1 64 0.2 relu 24.6 13.0 3.1 14.0 Table 1. Test table of BP-LSTM network model. 4 2 32 2 16 0.3 relu 35.3 18.9 3.6 16.1 5 2 64 2 32 0.2 sigmoid 76.7 39.2 5.5 25.7 WOB (kN) TOB (kN· m) 6 2 128 2 64 0.1 tanh 23.9 12.8 2.9 13.3 Lay- Neu- Activation 7 3 32 3 16 0.2 tanh 28.5 16.3 3.2 14.7 Layers==(BP) Neurons==(BP) Dropout RMSE==(kMAPE==RMSE==(k MAPE==( 8 3 64 3ers==(LSTM) 32 rons== 0.1(LSTM) relu Fu 27.1 nction 14.5 3.4 16.6 N) (%) N·m) %) 9 3 128 3 64 0.3 sigmoid 78.4 39.9 9.4 40.1 1 1 32 1 16 0.1 sigmoid 77.3 39.5 6.2 29.0 2 1 64 1 32 0.3 tanh 23.8 13.0 2.8 12.8 3 1 128 1 64 0.2 relu 24.6 13.0 3.1 14.0 4 2 32 2 16 0.3 relu 35.3 18.9 3.6 16.1 5 2 64 2 32 0.2 sigmoid 76.7 39.2 5.5 25.7 6 2 128 2 64 0.1 tanh 23.9 12.8 2.9 13.3 7 3 32 3 16 0.2 tanh 28.5 16.3 3.2 14.7 Appl. Sci. 2022, 12, x FOR PEER REVIEW 6 of 16 Appl. Sci. 2022, 12, x FOR PEER REVIEW 6 of 16 8 3 64 3 32 0.1 relu 27.1 14.5 3.4 16.6 8 3 64 3 32 0.1 relu 27.1 14.5 3.4 16.6 9 3 128 3 64 0.3 sigmoid 78.4 39.9 9.4 40.1 9 3 128 3 64 0.3 sigmoid 78.4 39.9 9.4 40.1 Appl. Sci. 2022, 12, 5282 6 of 16 Ca Cal lcula culatio tion n R Res esult ults s o of f WO WOB B a an nd d TOB TOB The The re resul sults ts o of f WOB WOB a an nd d T TOB OB a are re sh sho ow wn n in in Fi Figure gures s 2 2 a an nd d 3 3,, re respec spectively. tively. The The R RM MS SE E and MAPE of WOB is 23.8 kN and 13.0%, respectively. The RMSE and MAPE of TOB is and MAPE of WOB is 23.8 kN and 13.0%, respectively. The RMSE and MAPE of TOB is Calculation Results of WOB and TOB 2.8 kN· m and 12.8%, respectively. 2.8 kN· m and 12.8%, respectively. The results of WOB and TOB are shown in Figures 2 and 3, respectively. The RMSE The BP-LSTM neural network is used to realize the real-time prediction of WOB and The BP-LSTM neural network is used to realize the real-time prediction of WOB and and MAPE of WOB is 23.8 kN and 13.0%, respectively. The RMSE and MAPE of TOB is TOB, which lays a foundation for the real-time inversion of friction coefficient. 2.8 TOB, kN wh m and ich12.8%, lays a r espectively foundati.on for the real-time inversion of friction coefficient. Figure 2. Comparison of predicted and true WOB. Figure 2. Comparison of predicted and true WOB. Figure 2. Comparison of predicted and true WOB. Figure 3. Comparison of predicted and true TOB. Fig Figure ure 3 3.. Com Compa par ris ison on of of pr pre edi dic ct ted ed a an nd d t tr rue TOB ue TOB.. The BP-LSTM neural network is used to realize the real-time prediction of WOB and 3.1.2. Real-Time Inversion of Friction Coefficient 3.1.2. Real-Time Inversion of Friction Coefficient TOB, which lays a foundation for the real-time inversion of friction coefficient. 3.1.2. Real-Time Inversion of Friction Coefficient Torque and Drag Model Torque and Drag Model Torque and Drag Model The classical torque and drag models include soft string model [26] and stiff string The classical torque and drag models include soft string model [26] and stiff string The classical torque and drag models include soft string model [26] and stiff string model [27]. The soft string model without any consideration for the string stiffness is sim- model [27]. The soft string model without any consideration for the string stiffness is sim- model [27]. The soft string model without any consideration for the string stiffness is simple and ple ple applied a an nd d a applied pplied earlier, but ea earlier rlier it is ,,only but butsuitable it it is is o on n for ly ly vertical su suita itable ble wells f fo or r or ve ve wells rti rtica ca with l l well well small s s o oinclination. r r well wells s wi wit th h sm sma all ll in incli- cli- The stiff string model with considering the stiffness of string is more complex, but it is more nation. The stiff string model with considering the stiffness of string is more complex, but nation. The stiff string model with considering the stiffness of string is more complex, but suitable for extended reach wells, horizontal wells and other non-straight wells. The stiff it is more suitable for extended reach wells, horizontal wells and other non-straight wells. it is more suitable for extended reach wells, horizontal wells and other non-straight wells. string model is used for the real-time inversion of friction coefficient. The stiff string model is used for the real-time inversion of friction coefficient. The stiff string model is used for the real-time inversion of friction coefficient. The stiff string model is as follows: The stiff string model is as follows: The stiff string model is as follows: d( F) dk = E I k q cos a m n (7) b 1 t ds ds dF dF −− (( )) dk dk (7) =−EIk − qcos n (7) =−EIk − qcos n b b 1 1 tt ds ds ds ds Appl. Sci. 2022, 12, x FOR PEER REVIEW 7 of 16 dM bi = n (8) 2t ds 2 “±”: Negative for lifting condition, positive for lowering condition; F: axial load on Appl. Sci. 2022, 12, 5282 7 of 16 the drill string, N; S: depth, m; q: Gravity per unit length of drill string, N/m; 𝛼 : inclination angle, rad; EI: bending stiffness of drill string, N m ; 𝑛 : Contact force between drill string and wellbore, N/m; 𝜇 : Axial friction coefficient; 𝜇 Circumferential friction coefficient; 1 2 d M D bi = m n (8) 2 t 𝑘 : hole curvature, rad/m. ds 2 Calculation formula of borehole curvature 𝑘 : “”: Negative for lifting condition, positive for lowering condition; F: axial load on the drill string, N; S: depth, m; q: Gravity per unit length of drill string, N/m; a: inclination dd angle, rad; EI: bending stiffness of drill string, N m ; n : Contact force between drill string (9) k=+ sin b and wellbore, N/m; m : Axial friction coefficient; m Circumferential friction coefficient; 1 2 ds ds k : hole curvature, rad/m. Calculation formula of borehole curvature k : Calculation formula of contact force 𝑛 on drill string: 2 2 da df AB + k = + sin a (9) n = (10) ds ds 1+ Calculation formula of contact force n on drill string: dk qd 2 2 A= EI + k F− k −k M + EIk k + sin (11) A( + B ) b n b T b n n = (10) ds k ds 1 + m d dk q d d k q da B= −k M + EIk k + EIk − sin ( ) (12) A = E I + k bF Tk ( k Mb + n E I k k )n+ sin a (11) n n b b T b dd ss d ks ds k ds d dk q df B = ( k M + E I k k ) + E I k sin a (12) 22 n n b T b ds sin d d d d ds k ds1 d d k = − + cos +1 ! (13) n 2 2 2 2 2 2 2 k ds ds ds ds k ds ds sin a da d f df d a 1 da df bb k = + cos a + 1 (13) 2 2 2 2 ds ds ds ds ds ds k k b b 𝜙 : azimuth, rad; 𝑘 : borehole torsion, rad/m. f: azimuth, rad; k : borehole torsion, rad/m. Real-Time Inversion of Friction Coefficient; Real-Time Inversion of Friction Coefficient Taking the above four basic parameters into the torque and drag model, the real-time Taking the above four basic parameters into the torque and drag model, the real-time inversion of friction coefficient can be realized by dichotomy, as shown in Figure 4. The inversion of friction coefficient can be realized by dichotomy, as shown in Figure 4. The inversion inversion result result of o friction f fricticoef on c ficient oefficient is shown is shin ow Section n in Sec 3.3 ti .on 3.3. Figure 4. Flow chart of real time inversion for friction coefficient. Figure 4. Flow chart of real time inversion for friction coefficient. Appl. Sci. 2022, 12, x FOR PEER REVIEW 8 of 16 Appl. Sci. 2022, 12, x FOR PEER REVIEW 8 of 16 Appl. Sci. 2022, 12, 5282 8 of 16 3.2. Intelligent Prediction of Stuck Pipe Probability Based on LSTM 3.2. Intelligent Prediction of Stuck Pipe Probability Based on LSTM 3.2.1. Establishment of Stuck Sample 3.2. Intelligent Prediction of Stuck Pipe Probability Based on LSTM 3.2.1. Establishment of Stuck Sample Firstly, it is necessary to determine the stuck date and time according to the mudlog 3.2.1. Establishment of Stuck Sample data report, and then mark the normal sample and the stuck sample. Firstly, it is necessary to determine the stuck date and time according to the mudlog Firstly, it is necessary to determine the stuck date and time according to the mudlog Figure 5 shows the changes in hook tension and torque throughout the day on 2 May data report, and then mark the normal sample and the stuck sample. data report, and then mark the normal sample and the stuck sample. It can be seen that the time of stuck pipe is around 20:48:08 from the figure. Figure 5 shows the changes in hook tension and torque throughout the day on 2 May Figure 5 shows the changes in hook tension and torque throughout the day on 2 May It can be seen that the time of stuck pipe is around 20:48:08 from the figure. It can be seen that the time of stuck pipe is around 20:48:08 from the figure. Figure 5. Hook tension and torque changes in the whole day on 2 May. Figure 5. Hook tension and torque changes in the whole day on 2 May. Figure 5. Hook tension and torque changes in the whole day on 2 May. As shown in Figure 6, it is the change of hook tension and torque from 20:11:28 to As shown in Figure 6, it is the change of hook tension and torque from 20:11:28 to 21:21:28. During 20:50:28–20:51:28, the torque suddenly increases from 14.2 to 19.6 kN, As shown in Figure 6, it is the change of hook tension and torque from 20:11:28 to 21:21:28. During 20:50:28–20:51:28, the torque suddenly increases from 14.2 to 19.6 kN, which is consistent with the mudlog data report. Therefore, the accurate time of stuck pipe 21:21:28. During 20:50:28–20:51:28, the torque suddenly increases from 14.2 to 19.6 kN, which is consistent with the mudlog data report. Therefore, the accurate time of stuck pipe can be determined as 20:51:28. which is consistent with the mudlog data report. Therefore, the accurate time of stuck pipe can be determined as 20:51:28. can be determined as 20:51:28. Figure 6. Hook tension and torque changes from 20:11:28 to 21:21:28. Figure 6. Hook tension and torque changes from 20:11:28 to 21:21:28. Figure 6. Hook tension and torque changes from 20:11:28 to 21:21:28. The stuck pipe is a sudden accident, that is, the time from the beginning of the stuck pipe to the complete stuck pipe is very short, and sufficient time cannot be left to adjust The stuck pipe is a sudden accident, that is, the time from the beginning of the stuck the drilling parameters in time to avoid the stuck pipe. Therefore, it is necessary to mark pipe to the complete stuck pipe is very short, and sufficient time cannot be left to adjust the period before the stuck pipe as stuck pipe samples in order to achieve the purpose of the drilling parameters in time to avoid the stuck pipe. Therefore, it is necessary to mark forecasting in advance. The data of 20:28:28–20:50:28 are labeled as stuck pipe samples, the period before the stuck pipe as stuck pipe samples in order to achieve the purpose of and 20:11:28–20:27:28 are labeled as normal samples. forecasting in advance. The data of 20:28:28–20:50:28 are labeled as stuck pipe samples, and 20:11:28–20:27:28 are labeled as normal samples. Appl. Sci. 2022, 12, 5282 9 of 16 The stuck pipe is a sudden accident, that is, the time from the beginning of the stuck pipe to the complete stuck pipe is very short, and sufficient time cannot be left to adjust the drilling parameters in time to avoid the stuck pipe. Therefore, it is necessary to mark the period before the stuck pipe as stuck pipe samples in order to achieve the purpose of forecasting in advance. The data of 20:28:28–20:50:28 are labeled as stuck pipe samples, and 20:11:28–20:27:28 are labeled as normal samples. 3.2.2. Selection of Characteristic Parameters for Stuck Pipe Based on the mudlog data and the analysis of the factors affecting the stuck, we use 15 parameters: bit depth, hook tension, stand pipe pressure, torque, weight on bit, rpm, total pump stroke, inlet/outlet temperature, Inlet/outlet conductance, inlet/outlet density, inlet/outlet flow. 3.2.3. Training, Testing and Optimization of Intelligent Prediction Model for Stuck Pipe Generally, the optimal hyper-parameter combination is obtained through trial and error. We optimize the following parameters: time-stepping of the input data, the learning rate, the number of LSTM network layers, the number of LSTM neurons, and the activation function. In order to reduce the number of tests, the orthogonal test method (L18.3.5) is used to set the test plan [28]. The FAR (false alarm rate), MAR (missed alarm rate) and F1 are used to evaluate and optimize the model. The evaluation indexes of classification problems are shown in Table 2, The relevant calculation formulas are as follows. TP + TN Precison = (14) TP + FP FAR = 1 Precison (15) TP Recall = (16) TP + FN MAR = 1 Recall (17) 2 Precison Recall F1 = (18) Precison + Recall Table 2. Evaluation indexes of classification problem. Forecast Category Real Category Positive (Stuck) Negative (Non Stuck) Positive (Stuck) True Positive False Negative Negative (Non stuck) False Positive True Negative We combine FAR, MAR, F1 and model complexity to optimize the model. The evalua- tion indicators of each model are shown in Figure 7. F1 has been widely employed in information retrieval which can well evaluate the advantages and disadvantages of the classification model [29]. Therefore, our criterion for model selection is to select a model with low complexity when F1 are not significantly different. The larger the F1, the better the model. As shown in Figure 7a, the first, second, fourth, seventh, ninth, tenth, thirteenth, fifteenth and seventeenth models have higher F1, and the values are close to each other. Considering there are not many training samples, in order to prevent over fitting and improve the generalization ability of the model, as shown in Figure 7b, the first and the seventeenth model with lower complexity are selected. Appl. Sci. 2022, 12, x FOR PEER REVIEW 10 of 16 Appl. Sci. 2022, 12, 5282 10 of 16 (a) (b) (c) (d) Figure 7. Different evaluation indexes of classification model. (a) F1 of each model; (b) Complexity Figure 7. Different evaluation indexes of classification model. (a) F1 of each model; (b) Complexity of each model; (c) FAR of each model; (d) MAR of each model. of each model; (c) FAR of each model; (d) MAR of each model. In the process of drilling, we pay more attention to the MAR, that is, we can accept a F1 has been widely employed in information retrieval which can well evaluate the certain FAR, but cannot accept the MAR (all stuck can be predicted, but some non-stuck advantages and disadvantages of the classification model [29]. Therefore, our criterion for may be predicted as stuck). Therefore, when using the FAR and the MAR to optimize the model selection is to select a model with low complexity when F1 are not significantly model, the model with the lower MAR should be selected. As shown in Figure 7d, the first different. The larger the F1, the better the model. As shown in Figure 7a, the first, second, model with smaller MAR is selected as the best model. fourth, seventh, ninth, tenth, thirteenth, fifteenth and seventeenth models have higher F1, The prediction results of the best model are shown in Section 3.3. The prediction and the values are close to each other. Considering there are not many training samples, result is given by stuck pipe probability, and when the probability is greater than 0.4, it is in order to prevent over fitting and improve the generalization ability of the model, as considered as stuck pipe, otherwise it is not. shown in Figure 7b, the first and the seventeenth model with lower complexity are se- 3.3. Comprehensive Evaluation Method of Stuck Pipe Based on Fuzzy Mathematics lected. Through the analysis of Sections 3.1 and 3.2, two evaluation indicators of stuck pipe In the process of drilling, we pay more attention to the MAR, that is, we can accept a are finally obtained. One is the evaluation index based on the torque and drag model, that certain FAR, but cannot accept the MAR (all stuck can be predicted, but some non-stuck is, the friction coefficient, and the other is the evaluation index based on the data-driven may be predicted as stuck). Therefore, when using the FAR and the MAR to optimize the model, that is, the probability of stuck pipe. model, the model with the lower MAR should be selected. As shown in Figure 7d, the first The above two indicators can measure the possibility of stuck pipe to a certain extent. model with smaller MAR is selected as the best model. Considering that there are many fuzziness and uncertainty in drilling process, fuzzy The prediction results of the best model are shown in Section 3.3. The prediction re- mathematics theory is used to establish a comprehensive evaluation on the basis of the two sulsub-indices t is given by to r st ealize uck pipe compr pr ehensive obabilitevaluation y, and whof en stuck the pr pipe. obability is greater than 0.4, it is considered as stuck pipe, otherwise it is not. 3.3. Comprehensive Evaluation Method of Stuck Pipe Based on Fuzzy Mathematics Through the analysis of Sections 3.1 and 3.2, two evaluation indicators of stuck pipe are finally obtained. One is the evaluation index based on the torque and drag model, that Appl. Sci. 2022, 12, 5282 11 of 16 3.3.1. Establishment of Fuzzy Set for Stuck Pipe The American scientist Zadeh [30] extended the value of the ordinary set charac- teristic function from {0, 1} to [0, 1], thus creating the fuzzy set theory, and has the following definition: Let X be a space of points (objects), with a generic element of X denoted by x. Thus, X = {x}, if there is a real-valued function m , such that, m : X ! [0, 1] (19) Then A is a fuzzy set on X. In order to distinguish it from ordinary sets, the charac- teristic function m (x) is called a membership function. This function describes that the element x in the X belongs to the set A to the degree m (x). Different values of membership function m (x) correspond to different membership degrees of x to set A. When m (x) = 0, x does not belong to A at all; When m (x)= 1, x belongs to A A A completely; When 0 < m (x) < 1, x belongs to A to the extent of m (x). A A Based on the above fuzzy mathematics theory, the following fuzzy set of stuck pipe, S, can be established. The fuzzy set S indicates that “stuck pipe may occur”, Suppose that the membership degree of each element in the P = fP , P , , P g to the fuzzy set 1 2 n S is m (P ), m (P ), , m (P ), then the stuck pipe fuzzy set S can be expressed in the s s 2 s n following form: S = (m (P ), m (P ), , m (P )) (20) s s s n 1 2 P , P , , P are the various evaluation indexes of stuck pipe. Two evaluation indexes 2 n were used, friction coefficient and probability of stuck pipe. m (x) is the membership function of stuck pipe, and the final fuzzy set S can be simplified into the following form, S = (m (P ), m (P )) (21) s s 1 2 3.3.2. Determination of Membership Function For the stuck pipe fuzzy set, it is necessary to give the degree of membership of each stuck evaluation index to the fuzzy set S. Therefore, when using fuzzy mathematics theory, it is very important to find or design an appropriate membership function. The determi- nation of membership function is subjective. Different people will give different results for the same problem. Finally, the Sigmoid-type function is selected as the membership function of the stuck pipe fuzzy set. The range of the two sub-evaluation indexes in the fP , P g is between 0 and 1. Theo- 1 2 retically, when the two sub indexes are both small (between 0 and 0.5), it means that the final possibility of stuck pipe is very small at this time, that is, the possibility of stuck pipe obtained by the comprehensive evaluation index is also very small. However, when either of the two indexes is larger (0.5–1), it indicates that the possibility of stuck pipe is greater, that is, the probability of stuck pipe obtained by comprehensive evaluation index is greater. As shown in Figure 8, it can be found that the sigmoid function can simulate a similar situation, that is, when x is between 0 and 0.5, it can be simply considered that y increases linearly with x, when x is between 0.5 and 1, y increases exponentially with x. When there is basically no stuck pipe risk, the comprehensive evaluation index value for stuck pipe will be small. When there is a certain stuck pipe risk, the sigmoid function will further expand the possibility, that is, the comprehensive evaluation index will be larger. Appl. Sci. 2022, 12, x FOR PEER REVIEW 12 of 16 similar situation, that is, when x is between 0 and 0.5, it can be simply considered that y increases linearly with x, when x is between 0.5 and 1, y increases exponentially with x. Appl. Sci. 2022, 12, x FOR PEER REVIEW 12 of 16 When there is basically no stuck pipe risk, the comprehensive evaluation index value for stuck pipe will be small. When there is a certain stuck pipe risk, the sigmoid function will further expand the possibility, that is, the comprehensive evaluation index will be larger. similar situation, that is, when x is between 0 and 0.5, it can be simply considered that y increases linearly with x, when x is between 0.5 and 1, y increases exponentially with x. When there is basically no stuck pipe risk, the comprehensive evaluation index value for Appl. Sci. 2022, 12, 5282 12 of 16 stuck pipe will be small. When there is a certain stuck pipe risk, the sigmoid function will further expand the possibility, that is, the comprehensive evaluation index will be larger. Figure 8. Function curve in sigmoid form. 3.3.3. Establishment of Comprehensive Evaluation Index for Stuck Pipe After determining the membership function of the fuzzy set, a comprehensive index of stuck pipe can be constructed. The fuzzy set S is expressed as, Figure 8. Function curve in sigmoid form. Figure 8. Function curve in sigmoid form. S= (P), (P ) (22) ( ) 3.3.3. Establishment of Comprehensive Evaluation sIndex 1 fors Stuck 2 Pipe 3.3.3. Establishment of Comprehensive Evaluation Index for Stuck Pipe After determining the membership function of the fuzzy set, a comprehensive index of stuck pipe can be constructed. The fuzzy set S is expressed as, After determining the membership function of the fuzzy set, a comprehensive index x = ( ) (23) −− 6(x 1) of stuck pipe can be constructed. The fuzzy set S is expressed as, 1+ e S = (m (P ), m (P )) (22) s s 1 2 The value range of the two indexes 𝑃 and 𝑃 after the membership function are 1 2 S= (P), (P ) (22) ( ) s 1 s 2 m (x) = (23) between 0 and 0.5, so the two elements in 6 (th x e 1) stuck pipe fuzzy set can be simply linearly 1 + e added as the final comprehensive evaluation index, The value range of the two indexes P and P after the membership function are 1 2 x = (23) ( ) between 0 and 0.5, so the two elements in the stuck pipe fuzzy set can be simply linearly −− 6(x 1) 1+ e P =+ P P added as the final comprehensive evaluation index, ( ) ( ) (24) stuck S 1 S 2 The value range of the two indexes 𝑃 and 𝑃 after the membership function are 1 2 P = m (P ) + m (P ) (24) stuck S 1 S 2 As shown in Figure 9, the blue surface represents the surface composed of values of between 0 and 0.5, so the two elements in the stuck pipe fuzzy set can be simply linearly evaluation index 1 (friction coefficient,), evaluation index 2 (probability of stuck pipe) and As shown in Figure 9, the blue surface represents the surface composed of values of added as the final comprehensive evaluation index, comprehensive index. The red plane represents the threshold value of the comprehensive evaluation index 1 (friction coefficient,), evaluation index 2 (probability of stuck pipe) and comprehensive index. The red plane represents the threshold value of the comprehensive evaluation index. P =+ P P (24) ( ) ( ) stuck S 1 S 2 evaluation index. As shown in Figure 9, the blue surface represents the surface composed of values of evaluation index 1 (friction coefficient,), evaluation index 2 (probability of stuck pipe) and comprehensive index. The red plane represents the threshold value of the comprehensive evaluation index. Figure 9. Schematic diagram of comprehensive evaluation index surface and threshold plane. Figure 9. Schematic diagram of comprehensive evaluation index surface and threshold plane. In order to reduce the rate of missing alarm, the threshold value of comprehensive evaluation In ord index er to of re stuck duce pipe the isra set te to of 0.4, mis that sin is, g when alarm, the th compr e thre ehensive shold va evaluation lue of comprehensive index is less than 0.4, it is considered that there is basically no risk of stuck pipe. The evaluation index of stuck pipe is set to 0.4, that is, when the comprehensive evaluation smaller the index is, the smaller the probability of stuck pipe is. When the comprehensive Figure 9. Schematic diagram of comprehensive evaluation index surface and threshold plane. In order to reduce the rate of missing alarm, the threshold value of comprehensive evaluation index of stuck pipe is set to 0.4, that is, when the comprehensive evaluation Appl. Sci. 2022, 12, x FOR PEER REVIEW 13 of 16 Appl. Sci. 2022, 12, x FOR PEER REVIEW 13 of 16 index is less than 0.4, it is considered that there is basically no risk of stuck pipe. The index is less than 0.4, it is considered that there is basically no risk of stuck pipe. The smaller the index is, the smaller the probability of stuck pipe is. When the comprehensive Appl. Sci. 2022, 12, 5282 13 of 16 smaller the index is, the smaller the probability of stuck pipe is. When the comprehensive evaluation index is greater than 0.4, it is considered that there is a risk of stuck pipe. The evaluation index is greater than 0.4, it is considered that there is a risk of stuck pipe. The larger the index is, the greater the probability is. larger the index is, the greater the probability is. evaluation index is greater than 0.4, it is considered that there is a risk of stuck pipe. The 4. Results and Discussion larger the index is, the greater the probability is. 4. Results and Discussion The paper analyzes the stuck pipe case of well A in Tarim Oilfield, China. The stuck 4. Results and Discussion The paper analyzes the stuck pipe case of well A in Tarim Oilfield, China. The stuck pipe occurred at 6110.58 m. After various rescue measures, the accident was not success- The paper analyzes the stuck pipe case of well A in Tarim Oilfield, China. The stuck pipe occurred at 6110.58 m. After various rescue measures, the accident was not success- fully resolved, so it was finally decided to sidetrack again. It took about 3 months from pipe occurred at 6110.58 m. After various rescue measures, the accident was not successfully fully resolved, so it was finally decided to sidetrack again. It took about 3 months from the occurrence of the stuck pipe to the continuation of drilling, which seriously affected resolved, so it was finally decided to sidetrack again. It took about 3 months from the the occurrence of the stuck pipe to the continuation of drilling, which seriously affected the drilling efficiency. occurrence of the stuck pipe to the continuation of drilling, which seriously affected the the dFi rilli gure ng e 1f0 ficienc showy. s the stuck pipe index 1 (friction coefficient), which is calculated by drilling efficiency. the re Fi agure l-tim 1 e 0i n sh ve orsi ws oth n e mst eth uco k dpipe of f rict ind io ex n 1 coef (frictio ficient n coef esta fi blis cient), hed w in h ich Sec ti iso ca n lcula 3.1, a ted nd by its Figure 10 shows the stuck pipe index 1 (friction coefficient), which is calculated by the real-time inversion method of friction coefficient established in Section 3.1, and its change th cha e n re ge al- ca tim n cha e inra ve cte rsiriz one m the eth st ouck p d of f ipe ricttre ion n d coef to f aicient certa in esta exblis tent. hed in Section 3.1, and its can characterize the stuck pipe trend to a certain extent. change can characterize the stuck pipe trend to a certain extent. Figure 10. Variation trend of friction coefficient. Figure 10. Variation trend of friction coefficient. Figure 10. Variation trend of friction coefficient. Figure 11 shows the stuck pipe index 2 (stuck pipe probability), which is obtained Figure 11 shows the stuck pipe index 2 (stuck pipe probability), which is obtained from fromFi th gure e in tell 11 ig sh eo n w t s pr th ed e ictio stucn k m pipe odel ino d fex st uck 2 (stpipe uck pipe proba pr bili oba ty bili batsed y), wh on ic th he is L S oT bta Mi n ned et- the intelligent prediction model of stuck pipe probability based on the LSTM network in from the intelligent prediction model of stuck pipe probability based on the LSTM net- work in Section 3.2, which can provide early warning of stuck pipe through the changes Section 3.2, which can provide early warning of stuck pipe through the changes of mudlog work in Section 3.2, which can provide early warning of stuck pipe through the changes of mudlog data. The red straight line indicates the predicted result of stuck (stuck/non data. The red straight line indicates the predicted result of stuck (stuck/non stucking). Blue scatter of mudl indicates og datathe . The probability red straig ofh stuck t line pipe. indica The tes blue the straight predicted line re repr sulesents t of stthe uck real (stuck/non stucking). Blue scatter indicates the probability of stuck pipe. The blue straight line repre- sample of the site (0: no stuck, 1: stuck). stucking). Blue scatter indicates the probability of stuck pipe. The blue straight line repre- sents the real sample of the site (0: no stuck, 1: stuck). sents the real sample of the site (0: no stuck, 1: stuck). Figure 11. Intelligent prediction of stuck pipe probability. Figure 11. Intelligent prediction of stuck pipe probability. Figure 11. Intelligent prediction of stuck pipe probability. Figure 12 shows the comprehensive prediction of stuck pipe by using the comprehen- Figure 12 shows the comprehensive prediction of stuck pipe by using the compre- sive evaluation index established in Section 3.3. Figure 12 shows the comprehensive prediction of stuck pipe by using the compre- hensive evaluation index established in Section 3.3. hensive evaluation index established in Section 3.3. App Appl. l. SciSci. . 202022 22, 12 , 12 , x , 5282 FOR PEER REVIEW 14 of 16 14 of 16 Figure Figure 12. 12Pr . P ediction redictioof n stuck of stuc by k compr by comp ehensive rehenevaluation sive evaluindex. ation index. As shown in Figure 10, it is found that the friction coefficient increases gradually from As shown in Figure 10, it is found that the friction coefficient increases gradually 6000 m to 6110 m. The friction coefficient increases sharply from 0.35 to 0.75 around 6110 m, from 6000 m to 6110 m. The friction coefficient increases sharply from 0.35 to 0.75 around which indicates the risk of stuck pipe. However, Real-time inversion of friction coefficient 6110 m, which indicates the risk of stuck pipe. However, Real-time inversion of friction can only achieve qualitative evaluation, and it is difficult to accurately predict stuck pipe. coefficient can only achieve qualitative evaluation, and it is difficult to accurately predict It can be seen from Figure 11 that the evaluation indexes predicted by the intelligent stuck pipe. prediction model are: FAR: 0.3, MAR: 0, F1: 0.82. It can be found that although the MAR It can be seen from Figure 11 that the evaluation indexes predicted by the intelligent is 0, the FAR is relatively high, reaching 30%. Although a certain FAR is allowed for the prediction of stuck pipe, the FAR is too high, which will affect the drilling efficiency to a prediction model are: FAR: 0.3, MAR: 0, F1: 0.82. It can be found that although the MAR certain extent. is 0, the FAR is relatively high, reaching 30%. Although a certain FAR is allowed for the It can be seen from Figure 12 that the comprehensive evaluation indexes for stuck prediction of stuck pipe, the FAR is too high, which will affect the drilling efficiency to a pipe are: FAR: 0.01, MAR: 0.04, F1: 0.98. Compared with the intelligent prediction model, certain extent. the FAR is lower, only 1%. However, there is a certain MAR, which is 4%. Although for It can be seen from Figure 12 that the comprehensive evaluation indexes for stuck the prediction of stuck pipe, the existence of MAR will cause a certain risk to the site, this pipe are: FAR: 0.01, MAR: 0.04, F1: 0.98. Compared with the intelligent prediction model, paper has marked some normal samples as stuck samples when dividing stuck samples, the FAR is lower, only 1%. However, there is a certain MAR, which is 4%. Although for and it can be found from the figure that the 4% missed alarm rate is only the samples that the prediction of stuck pipe, the existence of MAR will cause a certain risk to the site, this is artificially marked as stuck samples are missed, and the real stuck samples have not been missed. paper has marked some normal samples as stuck samples when dividing stuck samples, As shown in Table 3, the three prediction methods are compared and analyzed. First of and it can be found from the figure that the 4% missed alarm rate is only the samples that all, trend analysis method of friction coefficient has a long history. In this paper, the neural is artificially marked as stuck samples are missed, and the real stuck samples have not network model is introduced to realize the real-time calculation of the WOB and TOB, been missed. and further realize the real-time monitoring and trend analysis of the friction coefficient As shown in Table 3, the three prediction methods are compared and analyzed. First during drilling, but it is still qualitative analysis, and it is difficult to give the accurate of all, trend analysis method of friction coefficient has a long history. In this paper, the quantitative index. neural network model is introduced to realize the real-time calculation of the WOB and T TOB, able 3. aComparison nd furtherof re thr ali ee ze pr th ediction e realmethods -time mof on stuck itoripipe. ng and trend analysis of the friction coef- ficient during drilling, but it is still qualitative analysis, and it is difficult to give the accu- Method FAR MAR F1 rate quantitative index. Qualitative Friction coefficient / / / Intelligent prediction 0.3 0.0 0.82 Table Quantitative 3. Comparison of three prediction methods of stuck pipe. Comprehensive evaluation 0.01 0.04 0.98 Method FAR MAR F1 The Qua intelligent litative prediction F of rict stuck ion cpipe oeffic based ient on LSTM network / can give / accurate / quantitative index of stuck pipe. IntHowever elligent pr , thr edic ough tion the analysis 0.3 of FAR, MAR 0.and 0 F1, it is 0.82 Quantitative found that the prediction of stuck pipe based on data-driven method has a high FAR of Comprehensive evaluation 0.01 0.04 0.98 30%, which will have a certain impact on the site. The comprehensive evaluation index for stuck pipe is obtained by combining two The intelligent prediction of stuck pipe based on LSTM network can give accurate stuck sub-indexes through fuzzy mathematics. It realizes the prediction of stuck pipe based quantitative index of stuck pipe. However, through the analysis of FAR, MAR and F1, it on data-driven and knowledge-driven model. Through the analysis of evaluation indexes is found that the prediction of stuck pipe based on data-driven method has a high FAR of 30%, which will have a certain impact on the site. The comprehensive evaluation index for stuck pipe is obtained by combining two stuck sub-indexes through fuzzy mathematics. It realizes the prediction of stuck pipe based on data-driven and knowledge-driven model. Through the analysis of evaluation indexes such as FAR, MAR, and F1, it is found that although the MAR is 4% (the missing Appl. Sci. 2022, 12, 5282 15 of 16 such as FAR, MAR, and F1, it is found that although the MAR is 4% (the missing is only the artificially marked stuck sample, not the real stuck sample), the FAR is only 1%, compared with the FAR obtained by intelligent method, the FAR is reduced by 96%, which greatly reduces the false alarm of stuck pipe. 5. Conclusions The prediction of stuck pipe is very challenging due to the hybrid nature of the drilling process (which consists of different activities), the variability of geological conditions, the combined occurrence of adverse events etc. Three prediction methods of stuck pipe are established. In the first method, the neural network technology is used to calculate WOB and TOB in real-time. Combined with the torque and drag model, the real-time inversion of the friction coefficient is realized. The analysis method of stuck pipe trend based on the friction coefficient is finally established. In the second method, intelligent prediction of stuck pipe probability is realized by using mudlog data and LSTM network. Finally, a comprehensive prediction model is established, which combines knowledge-driven model (the first method) with data-driven model (the second method) using fuzzy mathematics theory. For future work, we plan to look for more stuck pipe samples. On the one hand, we can increase the stability and generalization ability of the intelligent prediction model. On the other hand, we will use more samples to determine a reasonable threshold of stuck pipe instead of setting thresholds artificially. Author Contributions: Conceptualization, X.S. and S.Z.; methodology, S.Z., X.S. and Z.Z.; software, X.Y. and M.L.; validation, S.Z.; formal analysis, S.Z. and X.S.; investigation, S.Z. and Z.Z.; resources, M.L.; data curation, S.Z.; writing—original draft preparation, S.Z. and Z.Z.; writing—review and editing, S.Z. and X.S.; supervision, X.S.; funding acquisition, X.S. All authors have read and agreed to the published version of the manuscript. Funding: This research was funded by National Key Research and Development Program of China (funded by National Natural Science Foundation of China, No. 2019YFA0708300), the Strategic Coop- eration Technology Projects of CNPC and CUPB (funded by China National Petroleum Corporation, No. ZLZX2020-03), the National Science Fund for Distinguished Young Scholars (funded by National Natural Science Foundation of China, No. 52125401) and Science Foundation of China University of Petroleum, Beijing (funded by China University of petroleum, Beijing, No. 2462022SZBH002). Institutional Review Board Statement: Not applicable. Informed Consent Statement: Not applicable. Data Availability Statement: The data are not publicly available due to involve the information of Chinese oil fields and need to be kept confidential. Acknowledgments: The authors want to thank the National Natural Science Foundation of China and the CNPC for the financial support. 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