An Improved P-Wave Velocity-Stress Model for Rocks in Triaxial Compression Experiments

Abstract

ABSTRACT The acoustic velocity-stress equation of rocks is important to underground stress or pore pressure prediction. The P-wave velocity has different dependencies on stresses in different directions. An improved model between P-wave velocity and stress was established. P-wave velocity was measured for sandstone at both hydrostatic and differential stress up to 60MPa in the laboratory. P-wave velocity increases with increasing confining pressure and differential stress, at different rates. The proposed model can fit the P-wave velocity measurement results very well. It provides an approach to model the stress dependency of P-wave velocity for rocks under differential stress. INTRODUCTION The stress dependency of elastic wave velocity of rocks is important for many geophysical applications such as pore pressure prediction and hydrocarbon detection. However, uncertainty still exists and the need to overcome it has become more critical. In the past few years, the relationships between elastic wave velocity and the effective stress in rocks has been studied by many researchers and several analytical models have been put forward. Generally, elastic wave velocity increases with increasing effective stress (Katsuki et al., 2014). In previous studies, most laboratorial measurements of P-wave velocity were made at hydrostatic pressure (Vinciguerra et al., 2005). Accordingly, most of the empirical models only focused on the dependency of elastic wave velocity on the mean effective stress, which assumes that the stresses in different directions have the same effect on the elastic wave velocities. The most popular empirical relationship originally has the following form (Zimmerman et al., 1986): (Equation) where VP is the wave velocities, Pe is the mean effective stress, A, B, C, D are empirical parameters determined from velocity-stress data set. Greenfield et al. (1996) proposed another wave velocity-stress model: (Equation) Both models are founded on the classical elastic velocity equation, in which the square of wave velocity is proportional to the elastic moduli, and the assumption that the matrix second order elastic moduli are linear functions of stress over the range of interest, and use an inverse exponential relationship to fit the effect of crack closure. (Greenfield et al., 1996) In the next few years, Zimmerman's model was developed by many researchers (Eberhart-Phillips et al., 1989; Freund, 1992; Jones, 1995; Prasad & Manghnani, 1997; Khaksar et al., 1999; Carcione & Tinivella, 2001; Pervukhina et al., 2010) to fit elastic wave velocities for different types of rocks over a wide range of effective stress levels.