A statistical machine learning model to predict equivalent circulation density ecd while drilling, based on principal components analysis PCA

Mathematical equations, based on conservation of mass and momentum, are used to determine the ECD at different depths in the wellbore. However, such equations do not consider important factors that have a influence on the ECD such as: (i) bottom hole temperature, (ii) pipe rotation and eccentricity, and (iii) wellbore roughness. Thus, discrepancy between the calculated ECDs and actual ones has been reported in the literature. This paper aims to explore how artificial intelligence (AI) and machine learning (ML) could provide real-time accurate prediction of the ECD, to have more insight and management of wellbore downhole conditions. For this purpose, a supervised ML algorithm, support vector machine (SVM), based on principal components analysis (PCA), was developed. Actual field data of Well-1 including drilling surface parameters and ECDs, measured by downhole sensors, were collected to develop a classical SVM model. The dataset was split with an 80/20 training-testing data ratio. Sensitivity analysis with different SVM parameters such as regularization parameter C, gamma, kernel type (linear, radial basis function "RBF") was performed. The performance of the model was assessed in terms of root mean square error (RMSE) and coefficient of determination (R²). Afterward, PCA was applied to the dataset of Well-1 to develop an SVM model using the transformed dataset in PCA space. The performance of the model while using different numbers of principal components was evaluated. The results showed that the classical SVM with the linear kernel predicted the ECD with RMSE of 0.53 and R² of 0.97 in the training set, while RMSE and R² were 0.56 and 0.97 respectively in the testing set. The PCA-based SVM model, with the linear kernel and four principal components (93.53% variation of the dataset), predicted the ECD with RMSE 0.79 and R² of 0.95 in the testing set.