Artificial Intelligence Approaches to Modeling Equivalent Circulating Density for Improved Drilling Mud Management

Proper management of equivalent circulating density (ECD) plays a crucial role in drilling processes since poor control can lead to serious well control problems such as lost circulation and formation fracturing. Traditionally, ECD has been calculated using downhole tools or mathematical models. The novelty of this study lies in the use of fewer inputs for modeling, which enhances the simplicity and efficiency of the approach. Furthermore, several advanced machine learning models have been employed to predict ECD under standard conditions. The models utilized in this study demonstrated high adaptability to complex data and varying conditions, resulting in superior performance in predicting ECD compared to other models. Additionally, these models exhibited robustness to noisy and inconsistent data, enabling accurate predictions even in the presence of discontinuous and irregular data sets. Moreover, the empirical relationship developed in this study outperforms existing relationships in terms of accuracy, offering a more reliable and trustworthy predictive framework. To this goal, a data set containing 2367 field measurements from two wells in an Iranian oilfield using water-based fluids (WBF) was employed. Of these data, 70% was utilized for model development and training, while 30% was reserved for testing. Key variables influencing ECD, including standpipe pressure (SPP), rate of penetration (ROP), and surface mud weight (MW), were analyzed. Seven advanced machine learning algorithms were applied: cascade forward neural network (CFNN), generalized regression neural network (GRNN), wavelet neural network (WNN), and support vector regression (SVR) optimized with particle swarm optimization (PSO-SVR), farmland fertility algorithm (FFA-SVR), and grasshopper optimization algorithm (GOA-SVR). Additionally, a mathematical correlation was developed using the group method of data handling (GMDH). The results indicated that while all models accurately predicted ECD, the GOA-SVR algorithm provided the most reliable outcomes, with average absolute percent relative errors (AAPRE) values of 0.0823, 0.0975 and 0.0869% for the training, testing, and entire data sets, respectively. Moreover, the GMDH model demonstrated superior performance compared to other existing empirical models, especially when three key input variables were utilized. Additionally, the sensitivity analysis revealed that the surface mud weight had the most significant influence on ECD prediction. Finally, the leverage technique was implemented to assess the operational scope of the GOA-SVR and GMDH models. For the GOA-SVR model, 59 data points (∼2.5%) were identified as suspicious, while for the GMDH model, 29 data points (∼1.3%) were flagged. Additionally, 30 data points (∼1.3%) for GOA-SVR and 42 data points (∼1.8%) for GMDH were recognized as potential outliers, indicating that despite accurate predictions, these points fall outside the models’ applicability domain.