Experimental Investigation on Static and Dynamic Bulk Moduli of Dry and Fluid-Saturated Porous Sandstones

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.

Laboratory acousto-mechanical study into moisture-induced changes of elastic properties in intact granite

“…In laboratory ultrasonic tests, the P-wave velocity is widely observed to increase when macroporous, clay-deficient rocks become (almost) fully saturated with water. This P-wave velocity increase, under zero confining pressure, has been reported in sandstone as 8 to 73 % (King, 1966;Han, 1987;Coyner, 1984;Mavko & Jizba, 1991;Wang et al, 2021); granite as 8 to 27 % (Nur & Simmons, 1969;Saito, 1981;Coyner, 1984); limestone as 0 to 73 % (Nur & Simmons, 1969;Coyner, 1984;Agersborg et al, 2008) and dolomite as 28 % (Nur & Simmons, 1969). Various physical mechanisms have been proposed to predict such P-wave velocity increase; for example, Gassmann's equation ), Biot's theory (Biot, 1956) and the squirt flow model (Mavko & Jizba, 1991;.…”

Laboratory acousto-mechanical study into moisture-induced changes of elastic properties in intact granite

“…In laboratory ultrasonic tests, the P-wave velocity is widely observed to increase when macroporous, clay-deficient rocks become (almost) fully saturated with water. This P-wave velocity increase, under zero confining pressure, has been reported in sandstone as 8 to 73 % [22][23][24][25][26] ; granite as 8 to 27% 9,12,24 ; limestone as 0 to 73% 12,24,27 and dolomite as 28%. 12 Various physical mechanisms have been proposed to predict such P-wave velocity increase; for example, Gassmann's equation, 11 Biot's theory 28 and the squirt flow model.…”

Fault roughness controls injection-induced seismicity

“…Due to the high sample permeability (10 − 12 m 2 ), fluid pressure rapidly equilibrates on the order of milliseconds within the whole sample volume ( 46 , 58 ). With the onset of fluid injection, slip along smooth and rough faults initiates with a delay that progressively decreases with subsequent injection cycles (stage 3 in Fig.…”