A Novel Semi-Analytical Model of Rock Compressibility for Carbonate Formations

Abstract Over the past years, many researchers have studied the rock compressibility of porous media because it is the most crucial factor affecting the reservoir potential and recovery factor evaluation. However, it has yet to be definitive because the researchers differ, and some suggest it is a positive relationship with porosity, while others propose the opposite. Motivated by this disagreement, this study presents an empirical equation to estimate pore volume compressibility for carbonate formations. In this regard, this model was performed using several mathematical equations and one correlation. Thus, this equation was validated using laboratory tests. These tests were 415 laboratory-measured core porosity from the carbonate formation, which was utilized to estimate compressibility. In addition, twenty-one laboratory-measured cores compressibility were applied to test the model's accuracy. Well-log data were used to evaluate mechanical rock properties within a bulk modulus (dynamic and static). Moreover, the mechanical rock properties were estimated using derived equations suitable with three types of logs, including bulk density (ρb), compression wave velocity (DTC), and shear wave velocity (DTS). The elastic rock properties were validated using a uniaxial lab test to test the Static Young's Modulus correlation (Esta) validity, which is essential to derive the compressibility equation. The results led to a compressibility equation that was simple, uncomplicated, and easy to use. Moreover, this equation was compared with laboratory measurement results and confirmed accurate. The results were that the equation values were very close and compatible with laboratory measurements. Therefore, this equation is correct and robust and can be relied upon to estimate compressibility in the carbonate formation of the oilfields. The study's results could be a reference for carbonate formation to estimate compressibility and be used as effective cost tools.