Regularized ridge regression models to estimate static elastic moduli from wireline measurements: case study from Southern Iraq

Elastic moduli such as Young’s modulus (E), Poisson’s ratio (v), and bulk modulus (K) are vital to creating geomechanical models for wellbore stability, hydraulic fracturing, sand production, etc. Due to the difficulty of obtaining core samples and performing rock testing, alternatively, wireline measurements can be used to estimate dynamic moduli. However, dynamic moduli are significantly different from elastic moduli due to many factors. In this paper, correlations for three zones (Nahr Umr shale, Zubair shale, and Zubair sandstone) located in southern Iraq were created to estimate static E, K, and ν from dynamic data. Core plugs from the aforementioned three zones alongside wireline measurements for the same sections were acquired. Single-stage triaxial (SST) tests with CT scans were executed for the core plugs. The data were separated into two parts; training (70%), and testing (30%) to ensure the models can be generalized to new data. Regularized ridge regression models were created to estimate static E, K, and ν from dynamic data (wireline measurements). The shrinkage parameter (α) was selected for each model based on an iterative process, where the goal is to ensure having the smallest error. The results showed that all models had testing R2 ranging between 0.92 and 0.997 and consistent with the training results. All models of E, K, and ν were linear besides ν for the Zubair sandstone and shale which were second-degree polynomial. Furthermore, root means squared error (RMSE) and mean absolute error (MAE) were utilized to assess the error of the models. Both RMSE and MAE were consistently low in training and testing without a large discrepancy. Thus, with the regularization of ridge regression and consistent low error during the training and testing, it can be concluded that the proposed models can be generalized to new data and no overfitting can be observed. The proposed models for Nahr Umr shale, Zubair shale, and Zubair sandstone can be utilized to estimate E, K, and ν based on readily available dynamic data which can contribute to creating robust geomechanical models for hydraulic fracturing, sand production, wellbore stability, etc.