Development of New Mathematical Model for Compressional and Shear Sonic Times from Wireline Log Data Using Artificial Intelligence Neural Networks (White Box)

Abstract

Compressional (P-wave) and shear (S-wave) velocities are used to estimate the dynamic geomechanical properties including: Poisson’s ratio, Young’s modulus, and Lamé parameters. These parameters are mainly used in estimating the static properties of the formation rocks as well as the in situ stresses. The sonic logs are not always available, epically for old wellbores. Also, in several occasions when the sonic logs are available, missing sections found in the well logs might affect the analysis results. To the authors’ knowledge, there is no single straightforward correlation that can be used to accurately estimate both P- and S-wave travel times directly from the well log data. Most of the existing correlations use the P-wave velocity to measure the S-wave velocity. The main purpose of this study is to develop accurate and simple empirical models using wireline log data (bulk density, gamma ray, and neutron porosity) to predict the sonic travel times (P-wave and S-wave). These wireline logs are slandered wireline log data that are commonly recorded in most of the wells. Three robust artificial intelligence techniques, namely: support vector machine (SVM), artificial neural network (ANN), and adaptive neurofuzzy interference systems (ANFIS), were employed and compared based on their prediction performance. Ultimately, using the weights and biases of optimized ANN model, a simple generalized empirical correlation is derived that can be used without the need of costly commercial software’s to run the AI models. The obtained results showed that ANN, ANFIS, and SVM can be used to estimate P-wave and S-wave travel times. ANN outperformed the ANFIS and SVM by yielding the lowest average absolute percentage error (AAPE) and the highest coefficient of determination $\left( R^{2}\right)$ for predicting P-wave and S-wave travel times. ANN model could predict the P-wave and S-wave travel times from wireline log data with high accuracy giving $R^{2}$ of 0.98 when compared to actual field data. In addition, the developed empirical correlations prediction completely matched the ANNs prediction. The AAPE of the predicted P and S-waves travel times was less than 5%. The developed correlations are very accurate and can help geomechanical engineers to determine the dynamic geomechanical properties (Poisson’s ratio and Young’s modulus) and propose any operation in case where sonic logs are missing.