An experimental investigation of single Taylor bubbles rising in stagnant and downward flowing non-Newtonian fluids was carried out in an 80 ft long inclined pipe (4°, 15°, 30°, 45° from vertical) of 6 in. inner diameter. Water and four concentrations of bentonite–water mixtures were applied as the liquid phase, with Reynolds numbers in the range 118 < Re < 105,227 in countercurrent flow conditions. The velocity and length of Taylor bubbles were determined by differential pressure measurements. The experimental results indicate that for all fluids tested, the bubble velocity increases as the inclination angle increases, and decreases as liquid viscosity increases. The length of Taylor bubbles decreases as the downward flow liquid velocity and viscosity increase. The bubble velocity was found to be independent of the bubble length. A new drift velocity correlation that incorporates inclination angle and apparent viscosity was developed, which is applicable for non-Newtonian fluids with the Eötvös numbers ($E_0$) ranging from 3212 to 3405 and apparent viscosity (${\mu }_{app}$) ranging from 0.001 Pa∙s to 129 Pa∙s. The proposed correlation exhibits good performance for predicting drift velocity from both the present study (mean absolute relative difference is 0.0702) and a database of previous investigator’s results (mean absolute relative difference is 0.09614).

Early detection and characterization of anomalous events during drilling operations are critical to avoid costly downtime and prevent hazardous events, such as a stuck pipe or a well control event. A key aspect of real-time drilling data analysis is the capability to make precise predictions of specific drilling parameters based on past time series information. The ideal models should be able to deal with multivariate time series and perform multi-step predictions. The recurrent neural network with a long short-term memory (LSTM) architecture is capable of the task, however, given that drilling is a long process with high data sampling frequency, LSTMs may face challenges with ultra-long-term memory. The transformer-based deep learning model has demonstrated its superior ability in natural language processing and time series analysis. The self-attention mechanism enables it to capture extremely long-term memory. In this paper, transformer-based deep learning models have been developed and applied to real-time drilling data prediction. It comprises an encoder and decoder module, along with a multi-head attention module. The model takes in multivariate real-time drilling data as input and predicts a univariate parameter in advance for multiple time steps. The proposed model is applied to the Volve field data to predict real-time drilling parameters such as mud pit volume, surface torque, and standpipe pressure. The predicted results are observed and evaluated. The predictions of the proposed models are in good agreement with the ground truth data. Four Transformer-based predictive models demonstrate their applicability to forecast real-time drilling data of different lengths. Transformer models utilizing non-stationary attention exhibit superior prediction accuracy in the context of drilling data prediction. This study provides guidance on how to implement and apply transformer-based deep learning models applied to drilling data analysis tasks, with a specific focus on anomaly detection. When trained on dysfunction-free datasets, the proposed model can predict real-time drilling data with high precision, whereas when a downhole anomaly starts to build, the significant error in the prediction can be used as an alarm indicator. The model can consider extremely long-term memory and serve as the alternative algorithm to LSTM. Furthermore, this model can be extended to a wide range of sequence data prediction problems in the petroleum engineering discipline.

In this study, fluid viscosity effects on LSP performance in terms of boosting pressure were numerically investigated. A water–glycerin mixture with different concentrations corresponding to varying apparent viscosities was flowed through an in-house manufactured LSP under various flow conditions, e.g., changing flow rates, rotational speeds, and fluid viscosities. The pressure increment between the intake and discharge of the LSP was recorded using the differential pressure transducer. The same pump geometries, fluid properties and flow conditions were incorporated into the numerical configurations, where three-dimensional (3D), steady-state, Reynolds-averaged Navier–Stokes (RANS) equations with a standard SST (shear stress transport) turbulence model were solved by a commercial CFD code. With the high-quality poly-hexcore grids, the simulated pressure increment was compared with the corresponding experimental measurement. The internal flow structures and characteristics within the cavities contained by the LSP impeller and diffuser were also analyzed. The good agreement between the numerical results against the experimental data verified the methodology adopted in this study.