Novel semi-analytical model for estimating unconfined compressive strength in sandstone reservoirs: Implications for CO₂ sequestration

Unconfined compressive strength (UCS) is a critical parameter in the oil and gas industry, influencing drilling programs, cementing, well-completion design, and carbon capture and storage (CCS) projects. Accurate UCS estimation enhances operational safety and efficiency while reducing costs. Conventional determination from core sampling is expensive, time-consuming, and often limited by sample availability. Existing UCS correlations, typically derived from linear regression, frequently lack accuracy and consistency across diverse lithologies. This study introduces a semi-analytical UCS estimation model based on 2 porosity-driven equations anchored in fundamental rock mechanics. Using relationships involving bulk and shear modulus, the framework infers both dynamic and static elastic properties solely as functions of porosity. Validation against laboratory data from 75 core samples, supported by a direct cross-plot comparison between predicted and measured UCS, yields a coefficient of determination R² = 0. 9355 (95% CI: 0.912–0.955), demonstrating strong predictive capability compared to widely used global equations by Vernik, Sarda, and Edimann. The enhanced accuracy and robustness of the proposed model make it highly applicable for optimizing drilling, production, injection, and reservoir management operations. In CCS applications, precise UCS estimation is vital for assessing cap rock integrity, ensuring long-term CO 2 containment, and preventing leakage. As one of the few UCS estimation models derived primarily from first-principle mechanics, this approach offers a mathematically rigorous, porosity-only solution that reduces reliance on empirical regressions and is particularly advantageous in data-limited settings where machine learning (ML) models often suffer from overfitting and poor generalization. While the development and benchmarking of ML models are beyond the scope of this study, the proposed model achieves high predictive reliability with minimal input data while remaining physically interpretable and robust across varying geological conditions. This work addresses key challenges in subsurface mechanical property estimation and provides a valuable tool for drilling, petrophysics, reservoir engineering, and CCS operations. • Developed a semi-analytical model for UCS prediction using porosity and elastic properties in sandstone. • Achieved 84% prediction accuracy, outperforming traditional empirical models for geomechanical analysis. • Validated the model using 75 core samples from the Zubair Formation, demonstrating practical applicability. • UCS modeling supports CO₂ sequestration, wellbore stability, and sustainable subsurface resource management. • Provides a computationally efficient method adaptable to diverse sandstone formations and geological settings.