An Efficient Approach for Predicting Young’s Modulus of Sandstones Using Well Logs Without Shear-Wave Traveltime

The traditional method of determining the static Young’s modulus (Es) involves laborious and costly laboratory triaxial tests on rock samples. Using well logs, the Es is traditionally correlated to the dynamic Young’s modulus (Ed), estimated using both shear-wave traveltime (Δts) and compressional-wave traveltime (Δtc). However, without Δts data, the Es is often predicted using ad hoc, empirically developed correlations that are prone to significant errors. This work seeks a more efficient and precise alternative to these correlations. This endeavor employed dimensional analysis on a well-log suite to identify key factors influencing Young’s modulus, without relying on Δts data. Dimensional analysis identified three critical variables: acoustic Δtc, shale volume fraction (Vsh), and bulk density (ρb). A regression analysis was performed to develop a highly nonlinear model for predicting Young’s modulus based on the identified essential variables. The model was constructed using a development data set comprising 300 cored and logged depth intervals from a prominent shaly sandstone reservoir in the Middle East. The model achieved a remarkable average absolute relative error (AARE) of approximately 8.0% and a coefficient of determination (R2) of 0.95, demonstrating its high precision, reliability, and superior performance compared to existing literature models. Blind validation using 322 depth intervals from three heterogeneous shaly sandstone reservoirs confirmed the robustness of the developed nonlinear regression model, yielding an AARE of 13%. The model exhibited strong agreement with observed Es values and demonstrated reliable generalization across a wide range of lithologies and petrophysical conditions. A sensitivity analysis of the introduced model was conducted to evaluate the impact of each independent variable on predicting the Es. By omitting one variable at a time, the analysis revealed that sonic Δtc had the most significant impact on the results. Removing it caused the R² to drop from 0.95 to 0.37 and the AARE to rise from 8.0 to 26%. These results suggest that future efforts should focus on reducing errors linked to this variable to improve model accuracy and reliability. The Δtc for the delineated rock types proved adequate for predicting Young’s modulus, exhibiting a consistent exponential relationship between the two variables. A backpropagation neural network (BPNN) was developed to predict Es using the three input variables identified as dominant predictors. The model was trained and tested using the original model development data set and further validated on an independent data set, consisting of 120 cored and logged depth intervals, to assess its generalization capability. The BPNN architecture, optimized through systematic hyperparameter tuning, demonstrated strong predictive performance and robustness across varying petrophysical conditions. Compared to the nonlinear regression model, the BPNN showed enhanced accuracy in capturing complex nonlinear relationships, highlighting the promise of machine-learning approaches for reliable subsurface property estimation.