Numerical Upscaling of Seismic Signatures of Poroelastic Rocks Containing Mesoscopic Fluid-Saturated Voids

Abstract

We present a novel coupled fluid-poroelastic model and an associated numerical upscaling procedure to calculate seismic attenuation and velocity dispersion in porous rocks induced by fluid pressure diffusion (FPD) in the presence of mesoscopic fluid-saturated voids, such as, for example, vugs or factures. By applying appropriate interface conditions, the proposed model couples the Navier-Stokes equations for viscous fluids with Biot's equations of poroelasticity to model the mesoscopic voids and the embedding background, respectively. A finite element method is employed to solve the coupled problem for a set of three relaxation tests, which enables us to compute the complex-valued and frequency-dependent equivalent stiffness matrix of the considered synthetic sample. The newly proposed fluid-poroelastic approach is compared with a purely poroelastic one as well as a fluid-elastic approach in a benchmark model containing interconnected mesoscopic fractures embedded in a poroelastic background. We obtain excellent agreement for the proposed approach and the purely poroelastic model by optimizing the material properties of the fractures for the latter, which demonstrates both the correctness and advantages of our method over the purely poroelastic approach for modeling fluid-saturated mesoscopic voids. We also observe that, while the coupled fluid-elastic approach and the proposed method provide consistent results with regard to seismic attenuation due to the fracture-to-fracture FPD, the latter also allows to account for the effects of fracture-to-background FPD. Finally, we employ the proposed methodology to explore the seismic characteristics of a synthetic “vuggy” carbonate-type sample, for which we visualize and interpret the resulting seismic attenuation in terms of FPD between the microscopic and mesoscopic pores.