Analytical Method Based on Machine Learning (AM-BML) for a Cased Borehole under Anisotropic In-Situ Stresses in Formation

Abstract

In this work, an analytical method based on machine learning (AM-BML) is proposed to predict the stress distribution around a cased borehole in the formation with anisotropic in-situ stresses. Firstly, the stress field equations with undetermined coefficients are derived using the elasticity theory to formulate the stress field near the cased borehole. Secondly, the regression functions of a machine learning algorithm, least squares support vector machine (LS-SVM), are constructed according to the derived stress field equations. Thirdly, the undetermined coefficient equations are developed to determine the undetermined coefficients in the derived stress field equations according to the constructed LS-SVM regression functions and the derived stress field equations. The derived stress field equations and the developed undetermined coefficient equations together constitute the proposed AM-BML, which can well predict the stress distribution around a cased borehole in the formation with anisotropic in-situ stresses. Compared with the traditional analytical methods, the proposed AM-BML is more convenient for practical applications because it is difficult and complex to determine the undetermined coefficient in the stress field equations according to the traditional analytical methods. Finally, the proposed AM-BML is validated through the comparisons with numerical simulation experiments; and it is also used to investigate the influencing factors on the stress field of a cased borehole system, which gives some useful results. This work is helpful for the study of borehole stability and the other study related to the petroleum engineering.