Experimental Investigation on Static and Dynamic Bulk Moduli of Dry and Fluid-Saturated Porous Sandstones
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ORIGINAL PAPER
Experimental Investigation on Static and Dynamic Bulk Moduli of Dry and Fluid‑Saturated Porous Sandstones Lei Wang1,2 · Erik Rybacki1 · Audrey Bonnelye1 · Marco Bohnhoff1,2 · Georg Dresen1,3 Received: 3 April 2020 / Accepted: 8 September 2020 © The Author(s) 2020
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. Keyword Porous sandstone · Static bulk modulus · Dynamic bulk modulus · Narrow (compliant) cracks · Equant (stiff) pores
* Lei Wang wanglei@gfz‑potsdam.de 1
GFZ German Research Centre for Geosciences, Section 4.2 Geomechanics and Scientific Drilling, 14473 Potsdam, Germany
2
Department of Earth Sciences, Free University Berlin, 12249 Berlin, Germany
3
Institute of Earth and Environmental Science, University of Potsdam, 14469 Potsdam, Germany
List of Symbols Vbi , Vb, ΔVb Initial bulk volume of the rock sample, bulk volume of the rock sample at a given pressure and changed bulk volume of the rock sample with pressure, respectively Vpi , Vp, ΔVp Initial volume of void space, volume of void space at a given pressure and changed volume of void space with pressure (drained
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