Abstract
Knowledge of pressure-dependent static and dynamic moduli of porous reservoir rocks is of key importance for evaluating geological setting of a reservoir in geo-energy applications. We examined experimentally the evolution of static and dynamic bulk moduli for porous Bentheim sandstone with increasing confining pressure up to about 190 MPa under dry and water-saturated conditions. The static bulk moduli (Ks) were estimated from stress–volumetric strain curves while dynamic bulk moduli (Kd) were derived from the changes in ultrasonic P- and S- wave velocities (~ 1 MHz) along different traces, which were monitored simultaneously during the entire deformation. In conjunction with published data of other porous sandstones (Berea, Navajo and Weber sandstones), our results reveal that the ratio between dynamic and static bulk moduli (Kd/Ks) reduces rapidly from about 1.5 − 2.0 at ambient pressure to about 1.1 at high pressure under dry conditions and from about 2.0 − 4.0 to about 1.5 under water-saturated conditions, respectively. We interpret such a pressure-dependent reduction by closure of narrow (compliant) cracks, highlighting that Kd/Ks is positively correlated with the amount of narrow cracks. Above the crack closure pressure, where equant (stiff) pores dominate the void space, Kd/Ks is almost constant. The enhanced difference between dynamic and static bulk moduli under water saturation compared to dry conditions is possibly caused by high pore pressure that is locally maintained if measured using high-frequency ultrasonic wave velocities. In our experiments, the pressure dependence of dynamic bulk modulus of water-saturated Bentheim sandstone at effective pressures above 5 MPa can be roughly predicted by both the effective medium theory (Mori–Tanaka scheme) and the squirt-flow model. Static bulk moduli are found to be more sensitive to narrow cracks than dynamic bulk moduli for porous sandstones under dry and water-saturated conditions.
Highlights
The elastic moduli of rocks are important for many geotechnical applications, such as in design and construction of rock engineering projects, and in interpretation of seismic data in geophysical explorations
We examined experimentally the continuous evolution of static and dynamic bulk moduli for dry and water-saturated porous Bentheim sandstones deformed at hydrostatic pressure conditions
Static bulk moduli were calculated from pressure-volumetric strain curves and dynamic bulk moduli were obtained from ultrasonic wave velocities measurements (~ 1 MHz)
Summary
The elastic moduli of rocks are important for many geotechnical applications, such as in design and construction of rock engineering projects, and in interpretation of seismic data in geophysical explorations. There are, in general, two main methods used to determine the elastic moduli of rocks. Static moduli are derived from stress–strain relations in quasi-static rock compression tests performed on intact samples with very low loading rate (i.e., static method). Dynamic moduli of rocks are determined using measurements of ultrasonic wave velocities transmitting through the samples (Cheng and Johnston 1981). Dynamic elastic moduli are typically estimated using high-frequency ultrasonic wave velocities measurements, it is estimates of static elastic moduli that are widely employed for evaluating rock deformation, especially in rock excavation projects. Static and dynamic moduli of rock samples are commonly found to be different, understanding the underlying physical causes for the observed difference is crucial for utilizing both static and dynamic measurements
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