Experimental study of crack density influence on the accuracy of effective medium theory

Effective medium theory plays an important role in the characterization of fractured reservoirs. The main goal of this paper is to assess the accuracy of three classical effective medium theories (compliance-based non-interaction approximation, Hudson theory and anisotropic self-consistent approximation) and investigate their applicable frequency range. To evaluate the crack density limitation of these models, we construct a series of physical models with crack density varying from 0 to 12 per cent. To satisfy the long-wavelength approximation of effective medium theory, we consider a crack diameter and aperture of 3 and 0.12 mm, respectively. To study their appropriate high-frequency laboratory condition, we use the ultrasonic transmission method to measure the elastic wave velocities at frequencies of 500, 250 and 100 kHz. The experimental results are then compared with the effective medium theories to discuss their accuracy. We also highlight and compare the accuracy of these theories for the inversion procedure to quantify the crack density.