Machine learning models for equivalent circulating density prediction from drilling data

Equivalent circulating density (ECD) is considered a critical parameter during the drilling operation, as it could lead to severe problems related to the well control such as fracturing the drilled formation and circulation loss. The conventional way to determine the ECD is either by carrying out the downhole tool measurements or by using mathematical models. The downhole measurement is costly and has some limitations with the practical operations, while the mathematical models do not provide a high level of accuracy. Determination of the ECD should have a high level of accuracy, and therefore, the objective of this study is to employ machine learning techniques such as artificial neural networks (ANNs) and adaptive network-based fuzzy inference systems (ANFISs) to predict the ECD from only the drilling data with a high accuracy level. The study utilized drilling data from a horizontal drilling section that includes drilling parameters (penetration rate, rotating speed, torque, weight on bit, pumping rate, and pressure of standpipe). The models were built and tested from a data set that has 3570 data points, and another data set of 1130 measurements was employed for validating the models. The accuracy of the models was determined by key performance indices, which are the coefficient of correlation (R) and the average absolute percentage error (AAPE). The results showed the strong prediction capability for ECD from the two models through training, testing, and validation processes with R greater than 0.98 and a very low error of 0.3% for the ANN model, while ANFIS recorded R of 0.96 and AAPE of 0.7, and hence, the two models showed great performance for ECD estimation application. Also, the study introduces a newly developed equation for ECD determination from drilling data in real time.