The relationship between P-wave velocity and porosity in carbonate rocks shows a high degree of variability due to the complexity of the pore structure. This variability introduces high uncertainties to seismic inversion, amplitude variation with offset analysis, porosity estimation, and pore-pressure prediction based on velocity data. Elastic wave propagation in porous media is numerically modeled on the pore scale to investigate the effects of pore structure on P-wave velocities in carbonate rocks. We built 2D models of porous media using pore structure information and the similarity principle. Then, we simulated normal incidence wave propagation using finite element analysis. Finally, the velocity was determined from received modeled signals by means of crosscorrelation. The repeatability and accuracy of this modeling process was verified carefully. Based on the modeling results, a simple formulation of Sun’s frame flexibility factor (γk), aspect ratio (AR, the ratio of the major axis to the minor axis), and pore density was developed. The numerical simulation results indicated that the P-wave velocity increases as a power function as the AR increases. Pores with small AR (<0.1) or large γk created softening effects that decrease P-wave velocity significantly. The P-wave velocity of carbonate rocks was dispersive; it depends on the ratio of the wavelength to pore size (λ/d). Such scale-dependent dispersion was more evident for carbonate rocks with higher porosity, lower AR, and/or lower P-wave impedance of pore fluids. The P-wave velocity of carbonate rocks with complicated pore geometries (low AR, high γk, small d) was much lower than that of rocks with simple pore geometries (high AR, small γk, large d) at low and high λ/d. The pore-scale modeling of elastic wave properties of porous rocks may explain the poor velocity-porosity correlation in carbonate rocks.

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