Developing a semi-analytical model for estimating mechanical properties of sandstone reservoirs: Enhancing applications in hydrocarbon production and underground gas storage

Abstract

Rock mechanical properties, encompassing the static Young's modulus, bulk modulus, and shear modulus, influence strategic decision-making operations, such as drilling programs and well completion designs. When precisely calculated, these variables can significantly affect drilling cost-efficiencies and production economic returns. Even though these attributes are significant, the conventional estimation method is core-lab testing, which is expensive and limited to covering the entire reservoir strata. To address this challenge, we propose a new semi-analytical model with direct equations to estimate the elastic rock properties primarily anchored around porosity. In particular, we developed an analytical framework using generalized equations for bulk and shear modulus to calculate static rock mechanical properties as porosity-driven functions. We employed lab-tested core data from 55 core samples to validate the new model's efficiency. The model's innovative design allows computing all elastic properties solely based on porosity. Impressively, the results closely matched the lab measurements. The new semi-analytical model's equations yielded a good root mean square error (RMSE) in the calculated rock mechanical properties. Specifically, the new static Young's modulus equation has the lowest RMSE, 1.489, compared to 45.168 for the Edimann equation and 3.043 for the Zhang equation. The newly developed static shear modulus equation had an RMSE of 0.497, lower than Zhang's empirical equation's 1.262. However, the Zhang equation has an RMSE of 0.891 versus 2.029, slightly outperforming the new equation. According to the RMSE values, the discrepancy between the core sample-based measured, new semi-analytical model-calculated static modulus was caused by the fact that the core samples were collected from clean sand oil-bearing reservoir intervals. However, the derived equations used porosity ranges that covered shale and sand. In essence, the new semi-analytical model provides a fast and precise estimation of rock mechanical properties, easily solving drilling concerns. This research not only advances knowledge of drilling and geomechanics, but also makes strategies more efficient and cost-effective.