Elastic wave velocities in partially saturated rocks: Saturation hysteresis

All effective medium approach (differential self-consistent scheme) has been used to calculate elastic wave velocities in rocks containing spherical pores and ellipsoidal cracks with two fluid phases. The results are applied to the case of imbibition/drainage processes performed in the laboratory (at high frequencies). For that purpose, two scales of heterogeneities are accounted for. The first one corresponds to the size of pores or cracks. It is the scale of a dispersion mechanism termed ''local flow'' because it depends on local variations in pore/crack compressibility. The second scale, much larger, is controlled by the size of the heterogeneities of the fluid phase distribution. These heterogeneities are assimilated to pockets whose saturation is different from that of the surrounding medium. The pocket scale involves a second dispersion mechanism, often called ''global flow'' or ''pocket flow,'' which depends on fluid pressure equilibration among the regions which have distinct saturation levels. Our calculations include both mechanisms, each having its own characteristic scale. Imbibition is described through simple relations involving two parameters. The same is true for drainage. The predicted behavior for P wave velocities against saturation appears to be in good agreement with experimental data reported in the literature, for both drainage and imbibition.