Combining Insight from Physics-Based Models into Data-Driven Model for Predicting Drilling Rate of Penetration

During the drilling operations, optimizing the rate of penetration (ROP) is very crucial, because it can significantly reduce the overall cost of the drilling process. ROP is defined as the speed at which the drill bit breaks the rock to deepen the hole, and it is measured in units of feet per hour or meters per hour. ROP prediction is very challenging before drilling, because it depends on many parameters that should be optimized. Several models have been developed in the literature to predict ROP. Most of the developed models used drilling parameters such as weight on bit (WOB), pumping rate (Q), and string revolutions per minute (RPM). Few researchers considered the effect of mud properties on ROP by including a small number of actual field measurements. This paper introduces a new robust model to predict the ROP using both drilling parameters (WOB, Q, ROP, torque (T), standpipe pressure (SPP), uniaxial compressive strength (UCS), and mud properties (density and viscosity) using 7000 real-time data measurements. In addition, the relative importance of drilling fluid properties, rock strength, and drilling parameters to ROP is determined. The obtained results showed that the ROP is highly affected by WOB, RPM, T, and horsepower (HP), where the coefficient of determination (T2) was 0.71, 0.87, 0.70, and 0.92 for WOB, RPM, T, and HP, respectively. ROP also showed a strong function of mud fluid properties, where R2 was 0.70 and 0.70 for plastic viscosity (PV) and mud density, respectively. No clear relationship was observed between ROP and yield point (YP) for more than 500 field data points. The new model predicts the ROP with average absolute percentage error (AAPE) of 5% and correlation coefficient (R) of 0.93. In addition, the new model outperformed three existing ROP models. The novelty in this paper is the application of the clustering technique in which the formations are clustered based on their compressive strength range to predict the ROP. Clustering yielded accurate ROP prediction compared to the field ROP.

Establishment of data-driven multi-objective model to optimize drilling performance

Optimum drilling penetration rate, known as the rate of penetration (ROP) has played a big role in drilling operations. Planning the well ROP always becomes a challenge for drilling engineers to calculate the drilling time needed for the section. Optimum ROP is achieved when the time to drill the section is as planned.
 Many empirical approaches were develop to model the ROP based on the drilling parameters, and might not always match the actual ROP. In some cases, the actual ROP was slower than planned, which may increase the drilling cost, which needs to be avoided.
 Hence, some approaches using artificial intelligent (AI), and supervised machine learning have been develop to overcome it. Supervised machine learning is used to develop a ROP model and ROP prediction for one of the development fields, based only on two wells drilling parameters data. The model was train using Gradient Boosting, Random Forest, and Support Vector Machine. Drilling parameter test data then is used to validate the model. The model of Random Forest shows a good or promising result with R2 of 0.90, Gradient Boosting shows R2 of 0.86, and Support Vector Machine with R2 0.72. Based on the models generated, the Random Forest has shown good trend which could be used for modeling ROP in the future development wells.

The utilization of data-driven models in hydrology has witnessed a significant increase in recent years. The open-source philosophy underpinning much of the code developed and research being conducted has facilitated widespread access to the the hydrological community to sophisticated machine learning models and technology (Reichstein 2019). These data driven approaches to hydrological modelling has witnessed growing interest after multiple studies has shown how machine-learning models were able to outperform nationwide traditional physics-based hydrological models (Kratzerts et al. 2019). The latter often demands substantial man-hours for development, calibration and fine-tuning to accurately represent relevant hydrological processes. In this national-scale explorative study we undertake an in-depth examination of Danish catchment hydrology. Our objective is to understand what processes and dynamics are well captured by a purely data driven model without physical constraints, namely the Entity-Aware Long Short-Term Model (EA-LSTM). The model code was developed by Kratzerts et al. (2019) and the analysis build on top of a newly published national CAMELS data set covering 301 catchments in Denmark (Koch and Schneider, 2022), with an average resolution of 130 km2. Denmark, spanning an area of around 43 000 km2, demonstrates a relatively high data coverage. Presently more than 400 stations record water level measurements in the Danish stream network, while a network of 243 stations have collected meteorological data since 2011. These datasets maintained by the Danish Environmental Protection Agency and the Danish Meteorological Institute, respectively, and are publicly available. Despite Denmark’s data abundance, Koch and Schneider (2022) demonstrated that the data-driven EA-LSTM model, trained with the CAMELS dataset for Denmark (from now on referred to as the DK-LSTM) were not able to outperform the traditional physics-based hydrological model, against which it was benchmarked. Consequently, performance of the DK-LSTM model could be increased by pre-training it with simulations from a national physics-based model indicating that dominating hydrological processes are not described by the readily available input data in the CAMELS dataset. This study conducts a comprehensive analysis of Danish catchment hydrology aiming to explore three aspects: 1) the common characteristics of the catchments where the DK-LSTM performs well or encounters challenges, 2) the identification of hydrological characteristics, that exhibit improvement when informing the data-driven model with physics-based model simulations, and 3) an exploration of whether the aforementioned findings can guide us in determining necessary physical constraints and/or input variables that explains the hydrological processes for the data-driven model approach at a national scale, using the example of DK-LSTM.   Koch, J., and Schneider, R. Long short-term memory networks enhance rainfall-runoff modelling at the national scale of Denmark. GEUS Bulletin, 49. https://doi.org/10.34194/geusb.v49.8292, 2022. Kratzert, F., Klotz, D., Shalev, G., Klambauer, G., Hochreiter, S., and Nearing, G.: Towards learning universal, regional, and local hydrological behaviors via machine learning applied to large-sample datasets, Hydrol. Earth Syst. Sci., 23, 5089-5110, https://doi.org/10.5194/hess-23-5089-2019, 2019. Reichstein, M., Camps-Valls, G., Stevens, B. et al. Deep learning and process understanding for data-driven Earth system science. Nature 566, 195–204. https://doi.org/10.1038/s41586-019-0912-1, 2019.

For engineering simulation models, insufficient experimental data and imperfect understanding of underlying physical principles often make predictive models inaccurate. It is difficult to reduce the model bias effectively with limited information. To improve the predictive performances of the models, this paper proposes a new model updating strategy utilizing a data-driven model to integrate with a physics-based model. One of the main strengths of the proposed method is that it maximizes the utilization of existing limited information by combining physics-based and data-driven models built based on different principles. First, the physics-based model is updated via selecting a suitable updating method and updating formulation. A data-driven model is then constructed using the Gaussian process (GP) regression. Finally, a weight combination is employed to obtain the updated predictive model where the weights of experimental sites and non-experimental sites are determined by the minimum discrepancy of probability distributions of the posterior error and another data-driven model, respectively. The Sandia thermal challenge problem is used to demonstrate the effectiveness of the proposed method.

Measure-While-Drilling (MWD) data provide real-time insight into subsurface conditions and drilling performance, yet their complexity and operational noise often hinder reliable modeling. This study demonstrates the role of Exploratory Data Analysis (EDA) in developing robust machine learning (ML) models for lithology classification and penetration rate (PR) prediction in mining operations. A structured EDA workflow—comprising data integrity assessment, feature distribution analysis, correlation mapping, and depth-wise parameter profiling—was implemented to identify redundant attributes, isolate non-productive intervals, and enhance dataset consistency. Through EDA-informed normalization and feature selection, data consistency and model performance were significantly improved. Machine learning algorithms, including Decision Tree, Random Forest, and Multi-Layer Perceptron, were trained on the refined dataset. The Random Forest Classifier achieved 98.45% accuracy in lithology prediction, while the Random Forest Regressor produced the most accurate PR estimation (R2 = 0.83, RMSE = 0.52). These results highlight EDA as a critical foundation for constructing physics-informed, data-driven models that enhance predictive reliability and operational efficiency in mining environments.

Data-driven models have risen in popularity during the past 10 years, which increase the effectiveness and durability of systems without necessitating a lot of human involvement. Despite all of their advantages, they remain the limitations in terms of model interpretation, data selection, and model evaluation. Sensitivity analysis (SA) is a powerful tool to decipher behaviors of data-driven models to analyze the correlations among inputs and outputs of models, and quantify the severity of inputs’ influence on outputs to effectively interpret these black-box models. Feature selection (FS) is a preprocessing approach used in data-driven modeling to select the crucial parameters as inputs fed to models. For the most of the existing works, the FS is well used to select inputs through the analysis on the drilling data correlations, while SA is seldom employed for data-driven model evaluation and interpretation in drilling applications. Data-driven rate of penetration (ROP) models have consistently outperformed many conventional ROP models, most likely as a result of their strong data analysis capabilities, capacity to learn from data in order to recognize data patterns, and effective policies for making logical decisions automatically. A data-driven ROP model was developed from a benchmarking field drilling dataset in this work. Following the ROP modelling, sensitivity analysis methods were employed to identify the input variables that had the greatest influence on ROP estimations. The FS techniques and the sensitivity analysis were combined during the data preprocessing to identify the most important aspects for modelling. The outcomes demonstrate that using the robust sensitivity analysis techniques to overcome the limits of machine learning models allows for the best interpretation and understanding of the produced data-driven models.

The effect of formation thickness on the performance of deterministic and machine learning models for rate of penetration management in inclined and horizontal wells

The response patterns of riverbank to the components carried by different pollution sources in the river: Experiments and models

Offshore drilling with drill string over 10,000m long has many technical challenges. Among them, the challenge to control the weight on bit (WOB) between a certain range is inevitable for the integrity of drill pipes and the efficiency of the drilling operation. Since WOB cannot be monitored directly during drilling, the tension at the top of the drill string is used as an indicator of the WOB. However, WOB and the surface measured tension are known to show different features. The deviation among the two is due to the dynamic longitudinal behavior of the drill string, which becomes stronger as the drill string gets longer and more elastic. One feature of the difference is related to the occurrence of high-frequency oscillation. We have analyzed the longitudinal behavior of drill string with lumped-mass model and captured the descriptive behavior of such phenomena. However, such physics-based models are not sufficient for real-time operation. There are many unknown parameters that need to be tuned to fit the actual operating conditions. In addition, the huge and complex drilling system will have non-linear behavior, especially near the drilling annulus. These features will only be captured in the data obtained during operation. The proposed hybrid model is a combination of physics-based models and data-driven models. The basic idea is to utilize data-driven techniques to integrate the obtained data during operation into the physics-based model. There are many options on how far we integrate the data-driven techniques to the physics-based model. For example, we have been successful in estimating the WOB from the surface measured tension and the displacement of the drill string top with only recurrent neural networks (RNNs), provided we have enough data of WOB. Lack of WOB measurement cannot be avoided, so the amount of data needs to be increased by utilizing results from physics-based numerical models. The aim of the research is to find a good combination of the two models. In this paper, we will discuss several hybrid model configurations and its performance.

A model for predicting sand erosion in 90 degree elbows and bends has been developed based on computational fluid dynamics (CFD), particle tracking and erosion data. After the flow field was obtained from the flow (CFD) model, particles were introduced into the flow and particle trajectories were computed using a Lagrangian approach. A model was also implemented that accounts for the interaction between the particles and the target material. Based on predicted particle impingement velocities, erosion rates and penetration rates were predicted using the empirical equations for erosion ratio. The predicted penetration rates are compared with available experimental data for several different elbows. The agreement between the predicted penetration rates and the experimental data is good. The erosion model is applied to standard (short-radius) elbows and long-radius elbows to understand why long radius elbows have lower erosion (penetration) rates. In addition, based on many predictions and erosion rate results, a new CFD based correlation is developed and is recommended as a first-order approximation for engineering calculations to account for effects of elbow radius on erosion in long-radius elbows. This equation is for computing the ratio of the wall thickness loss (or the penetration rate) in a long-radius elbow to the penetration rate of a standard (short-radius) elbow. The results from the correlation agree well with the trend of available data in the literature.

Physics-informed ensemble learning with residual modeling for enhanced building energy prediction

Higher rate of penetration (ROP) indicates successful drilling operation but is not the only drilling success measure. However, Conventional ROP prediction methods focus on increasing ROP and neglect the hole cleaning state, which can be altered by ROP changes. Higher ROP in vertical and deviated wells may increase cutting concentration, leading to hole cleaning problems such as overpulling and stuck pipe. With this problem in mind, this paper utilized geological, rheological, and drilling data of 31 vertical wells across four oil fields located in the Egyptian Western Desert, developed intelligent ROP prediction model through back propagation neural network (BPNN), and compared the proposed BPNN results with an empirical model. Finally, the pattern recognition algorithms including discriminant analysis, support vector machines, and neural network pattern recognition (NNPR) were implemented to discriminate hole cleaning efficiency following the ROP prediction process. Recognition models were developed based on predicted ROP, bit wear rate, specific energy, and drilling fluid carrying capacity index to evaluate hole cleaning. The accuracy of the multi-strategy classifier was evaluated using area under curve, confusion matrix, and receiver operating characteristic. The BPNN model outperformed the empirical model in terms of linear correlation coefficient (R = 98.6%) and average absolute error (AAE = 5.5%). Additionally, the best classification performance was achieved using the NNPR algorithm with 91% accuracy and a cross-validation error equal to zero. For validity, the proposed approach predicted ROP and classified hole cleaning efficiency for new vertical well in adjacent oil field, resulting in a 6% improvement in ROP.

Many researches on the prediction of the penetration rate of the tunneling boring machine (TBM) have been carried out. The prediction of the penetration rate will contribute to reduce the danger of TBM construction, decrease the cost and provide the support for the construction planning. Most methods for predicting penetration rate rely on the fixed equation relationship between the input parameters and output parameters. In this paper, we build up a dynamic model. We mainly make use of the partial least squares regression algorithm (PLS) and the structure of the fuzzy-neuron network (FNN) to build up the model. All the data should be normalized. We randomly select 120 groups of the data from TBM construction as the training data and 33 groups of data as the testing data. The training and testing results are analyzed by the mean square error and the correlation coefficient. At the same time, we compare the prediction of the PLS-FNN model with the prediction of the FNN model. The simulation result shows that the PLS-FNN model has the good performance for the prediction.

Using a neural network – Physics-based hybrid model to predict soil reaction fronts