Estimation of static Young’s modulus for sandstone formation using artificial neural networks

Abstract

In this study, we used artificial neural networks (ANN) to estimate static Young’s modulus (Estatic) for sandstone formation from conventional well logs. ANN design parameters were optimized using the self-adaptive differential evolution optimization algorithm. The ANN model was trained to predict Estatic from conventional well logs of the bulk density, compressional time, and shear time. The ANN model was trained on 409 data points from one well. The extracted weights and biases of the optimized ANN model was used to develop an empirical relationship for Estatic estimation based on well logs. This empirical correlation was tested on 183 unseen data points from the same training well and validated using data from three different wells. The optimized ANN model estimated Estatic for the training dataset with a very low average absolute percentage error (AAPE) of 0.98%, a very high correlation coefficient (R) of 0.999 and a coefficient of determination (R2) of 0.9978. The developed ANN-based correlation estimated Estatic for the testing dataset with a very high accuracy as indicated by the low AAPE of 1.46% and a very high R and R2 of 0.998 and 0.9951, respectively. In addition, the visual comparison of the core-tested and predicted Estatic of the validation dataset confirmed the high accuracy of the developed ANN-based empirical correlation. The ANN-based correlation overperformed four of the previously developed Estatic correlations in estimating Estatic for the validation data, Estatic for the validation data was predicted with an AAPE of 3.8% by using the ANN-based correlation compared to AAPE’s of more than 36.0% for the previously developed correlations.