Modeling the Acoustic Hysteresis of P and S Wave Velocity

Acoustic velocity in rocks is strongly depends on pressure, indicating that wave propagation is very nonlinear and the quasistatic elastic properties of rocks are hysteretic. Characterization of hysteretic behavior is important for a mechanical understanding of reservoirs during depletion. Therefore a quantitative model - which provides the physical explanation - of the mechanism of pressure dependence is required. In this paper a petrophysical model is presented which describes the connection between the propagation velocity of acoustic wave and rock pressure both in case of pressurization and depressurization cycles as well as explains the mechanism of acoustic hysteresis. The developed model is based on the idea that the pores in rocks close during pressurization and reopen during depressurization. It is valid also for S wave velocities since the basis of the model is the change of pore volume. The model was applied to acoustic P and S wave velocity data sets. The parameters of the petrophysical model were determined by a linearized inversion method. The calculated data matched accurately with measured data proving that the new rock physical model describing acoustic hysteresis applies well in practice.