The effect of confining pressure on elastic wave velocities and dynamic to static Young’s modulus ratio Mohammad Reza Asef 1 and Ali Reza Najibi 1 ABSTRACT We carried out laboratory experiments under dry conditions on limestone core specimens of Sarvak formation obtained from an oil well in the southwest of Iran. Our objective was to study the effect of confining pressure on the compressional and shear wave velocities (V P , V S ), and on the dynamic to static Young’s modulus ratio (E d ∕E s ). Furthermore, we made attempts to pre- dict V P and V S at atmospheric pressure based on the same ve- locities at various confining pressures. These analyses revealed that, below a critical pressure with an increase in confinement V P and V S increased exponentially, representing a poroelastic regime. Above a critical pressure, however, the trend was linear. Likewise, we observed that with an increase in confinement, E d ∕E s initially decreased exponentially, followed by a linear decreasing trend above the critical pressure. This indicated that E s is more responsive than E d . Accordingly, these observations infer that it is possible to predict E s based on E d at different confining stresses. This is an important improvement for geo- mechanical modeling of hydrocarbon and geothermal reservoirs because static parameters are more realistic input parameters. Besides, we derived the coefficients of the velocity-pressure equation for Sarvak limestone using least square regression analysis. More interestingly, we predicted V P and V S at atmo- spheric pressure based on these coefficients. Good agreement was observed between measured and predicted velocities at atmospheric pressure. Analysis of similar published experi- ments on oceanic basalts strongly confirmed these observations. INTRODUCTION Young’s modulus (E) is a key rock mechanical parameter, and the most frequently used in estimating in situ stresses, hydrocarbon re- servoir compaction evaluation, and wellbore stability analysis (Chang et al., 2006). For its measurement based on standard labora- tory experiments, a uniaxial static load is gently applied on the rock specimen. Simultaneously, the elastic deformation is measured and recorded. The slope of the stress-strain curve is known as the mod- ulus of elasticity or the static Young’s modulus (E s ). Likewise, compressional and shear waves (also known as elastic, sound, or ultrasonic waves) depend explicitly on the elastic moduli of rock. This is obviously because rock material will experience similar stresses (with lower amplitude) when an acoustic wave passes by (Fjaer et al., 2008). Accordingly, dynamic Young’s modulus (E d ) is determined, knowing the compressional and shear wave velocities (V P and V S , respectively) as well as the rock density (ρ) expressed in the form of equation 1 E d ¼ ρ:V 2 S 3V 2 P − 4V 2 S V 2 P − V 2 S : (1) Input parameters of this equation (V P , V S , and ρ) may be mea- sured in the lab and in the field using the well-established sonic and density logs. Nevertheless, E d is generally different from E s (Fjaer et al., 2008). One of the most important reasons for this phenom- enon is the lower strain amplitude encountered in the process of dynamic experiments (Zimmer, 2003). In fact, during the static loading, a large stress level is applied to the rock grains, such that in turn it can close pore spaces and microcracks at the initial state of the applied stress. Accordingly, during the static loading, the mea- sured strain amplitude is typically at the order of 10 −2 to 10 −3 , whereas in case of dynamic loading, a significantly lower level of stress is applied. Therefore, the strain amplitude measures about 10 −6 or 10 −7 (Figure 1). However, the static and dynamic moduli are equal for a homogeneous, elastic material like steel (Ledbetter, 1993). Thus, the physical origin of this discrepancy seems to be Manuscript received by the Editor 20 July 2012; revised manuscript received 9 December 2012; published online 10 April 2013. 1 Kharazmi University, Department of Geology, Tehran, Iran. E-mail: asef@khu.ac.ir; najib.alirezai@gmail.com. © 2013 Society of Exploration Geophysicists. All rights reserved. D135 GEOPHYSICS, VOL. 78, NO. 3 (MAY-JUNE 2013); P. D135–D142, 11 FIGS., 8 TABLES. 10.1190/GEO2012-0279.1 Downloaded 05/17/13 to 78.39.184.233. Redistribution subject to SEG license or copyright; see Terms of Use at http://library.seg.org/