## Rock physics models for cracked media

### Zimin Zhang, Robert R. Stewart

Two rock physics models for cracked media are investigated in this paper: the Kuster-Toksz model for randomly oriented cracks, and Hudson's model for aligned cracks. The effects of crack shape, aspect ratio and crack density are discussed using rock properties from several field locations: Ross Lake heavy oil field, Saskatchewan, Violet Grove Alberta CO_{2} injection site, and a Saskatchewan mining area.

Inclusion shape has a large influence on the effective rock properties from the Kuster-Toksz model. Generally, smaller aspect ratios (thinner cracks) yield larger drops of moduli and velocities. For oblate spheroid and penny shape inclusions, approximate /c (aspect ratio/volume concentration) values should not be smaller than 0.4 (equivalent to c2.5). As for penny shape inclusion, a valid maximum /c values exists and changes drastically with respect to the concentration value c. The upper /c value limit decreases with c. For Hudson's model, smaller aspect ratio cracks have a smaller valid crack density range, especially for Vs, of approximately 0.05 (equivalent to a crack porosity of about 0.1%) for cracks with an aspect ratio of 0.002.

Based on the modeling results for rocks from the chosen areas, 1% porosity due to penny shape cracks with an aspect ratio of 0.01 can produce velocity decreases of up to 22% from Hudson's model, and 16% P-velocity and 11% S-velocity decreases from the Kuster-Toksz model. The results also indicate that the percentage changes of S-velocity from both models and P-velocity along crack planes from Hudson's method have almost no dependence on uncracked rock properties. The percentage changes of P-velocity (P-velocity along the crack normal for Hudson's model) are consistent with values of uncracked rocks for the Kuster-Toksz model and Hudson's method without fluid substitution. Finally, anisotropic fluid substitution introduces a higher percentage of P-velocity changes and similar S-velocity changes.