Study of the variation of drilling mud density with temperature, pressure, and circulation rate using artificial neural networks, statistical models, and empirical correlations

Abstract

Well control is an important aspect of drilling operations because improper well control can result in kicks and blowouts with grave consequences. A successful well control requires a good understanding of the relationships between drilling mud pressure and formation pressure, as well as the variation of bottom hole pressure during drilling operations. As the hydrostatic pressure of the drilling mud column accounts for most of the pressure, a more accurate control of the changes of mud density will contribute to a more accurate bottom hole pressure modeling. Regarding the control of the mud density, a practical problem has existed so far in petroleum drilling: the mud density is determined at the surface condition, and its values vary along the depth of the well because of the changes of temperature and pressure, which consequently leads to an inaccuracy in mud density control in reality.

In order to reduce the inaccuracy in mud density control, this research aims to provide a reliable method to correctly predict the drilling mud’s density under specific conditions. Different artificial neural networks (ANN) were proposed to predict drilling mud density based on the value of mud density at surface conditions, circulation rate, bottomhole pressure, and temperature. This study then used statistical methods to compare the predicted results with results obtained from existing empirical correlations and from other researchers’ works to find out the most optimal artificial neural network which should consist of only one hidden layer. The main contributions of this research in comparison with existing papers are that: 1) Existing methods did not take into account the influence of circulation rate, therefore the real working conditions of the drilling mud were not represented entirely. Our research included the circulating rate in the ANN modeling and in the study of relative importance. The results indicated that the value of mud density at surface conditions had the greatest effect on the prediction results, and the influence of the circulating pump flow rate is small but should not be ignored; 2) Our research used different methods (ANN, Generalized Additive, Nonlinear Function) to predict the mud density in variation with temperature and pressure, which has never been approached in existing literature; 3) The sufficiency in the number of data was studied in this research, which has never been treated in previous studies. The Bootstrap method was used in this regard; 4) We remarked that the overfitting has not been treated properly in the existing literature review in this field, hence we included a thorough analysis of the overfitting in this paper.  Finally, the results of this paper can be useful in real life because it can help drillers to accurately predict the mud density under varied conditions of pressure and temperature, and therefore to increase the safety of the drilling operations.