A novel semi-analytical model for pore volume compressibility in oil-bearing sandstone formations

Rock compressibility is an essential parameter in many petroleum engineering applications, specifically in reservoir modeling. It is an independent variable that is not measured in conventional core analysis but can be estimated through correlations or using hydrostatic or triaxial tests (if available). In this research, a new semi-analytical model was reconstructed to estimate the isothermal rock compressibility in sandstone formations. The newly derived model was validated using raw data collected from the upper sandstone member/Zubair formation of several oil fields in southern Iraq. In this research, analytical equations and some empirical correlations were used to formulate a semi-analytical model to predict the isothermal rock compressibility. The derivation started with the equations of dynamic elastic properties of Young's Modulus and Poisson's ratio parameters to derive the static state of these two parameters. Specifically, Johan Fuller's correlation was utilized to find the static Young's Modulus, which was used with Poisson's ratio to compute the static bulk modulus. In the final step of the derivation, the compressibility equation was simplified to be a function of porosity only, which eliminates the effect of the static bulk modulus. The predictions of the derived model were compared with laboratory test measurements of pore volume compressibility, porosity, and elastic rock properties, and an acceptable matching was achieved. To support the accuracy and robustness of the new model, the results were compared with several available empirical correlations, and better matching was obtained by computing the Absolute Percent Error (AAPE), Mean Square Error (MSE), and Absolute Root MSE (ARMSE). Consequently, the new pore volume compressibility equation matches lab-measured data significantly. However, the lab-measured data showed poor compatibility with available equations in the literature. Therefore, this model should be accurate and robust for compressibility estimation in other oil-bearing consolidated and unconsolidated sandstone formations. Additionally, the newly derived equation is simple, uncomplicated, and easy to use.