Modeling of Viscoelastic Properties of Porous Rocks Saturated with Viscous Fluid at Seismic Frequencies at the Core Scale

Abstract:

Currently the moduli and velocities of rocks at seismic frequencies are usually measured by the strain-stress method in lab. However, such measurements require well-designed equipment and skilled technicians, which greatly hinders the experimental investigation on the elastic and visco-elastic properties of rocks at seismic frequencies. We attempt to model the dynamic moduli of porous rocks saturated with viscous fluid at seismic frequencies on core scale using the strain-stress method, aiming to provide a complement to real core measurements in lab. First, we build 2D geometrical models containing the pore structure information of porous rocks based on the digital images (such as thin section, SEM, CT, etc.) of real rocks. Then we assume the rock frames are linearly elastic, and use the standard Maxwell spring-dash pot model to describe the visco-elastic properties of pore fluids. Boundary conditions are set according to the strain-stress method; and the displacement field is calculated using the finite element method (FEM). We numerically test the effects of fluid viscosity, frequency, and pore structure on the visco-elastic properties based on the calculation results. In our modeling, the viscosity of the pore fluid ranges from 10³mPas to 10⁹mPas; and the frequency varies from 5Hz to 500Hz. The preliminary results indicate that the saturated rock behaves stiffer and shows larger phase lag between stress and strain when the viscosity of the pore fluid and (or) the frequency increase.