Numerical investigation of the correlations of hydraulic and elastic characteristics in diverse carbonate rock types

Abstract Carbonate reservoirs are vital energy storage spaces, including for oil, shale gas, geothermal, and hydrogen energy. Accurate prediction of reservoir characteristics such as permeability and saturated fluid types through noninvasive approaches is crucial for optimal storage capability. In this paper, we combine a linear Boolean model and a discrete Fourier transform approach to generate pore‐ and fracture‐pore‐type carbonate rocks. Elastic wave velocity information is necessary to predict permeability in different rock geometry models. Permeability is calculated using the lattice Boltzmann method, and the elastic wave velocity is calculated using a finite element method based on a minimal energy approach. Saturated fluids that contain oil and gas were both considered. Our simulated results reveal that, for pore‐type carbonate, empirical formulas were proposed to estimate permeability through elastic data. However, in fracture‐pore carbonate rocks, the precision of the empirical formula is compromised due to the presence of significant conductive channels within the rock matrix. We also find that using S‐wave velocity and permeability relationships to distinguish oil and gas is better than using P‐wave velocity and permeability relationships under low‐porosity conditions.