Finite-difference modeling of wave propagation and diffusion in poroelastic media

Author:

Wenzlau Fabian12,Müller Tobias M.12

Affiliation:

1. Universität Karlsruhe (TH), Geophysical Institute, Karlsruhe, Germany. .

2. CSIRO Petroleum, Perth, Australia. .

Abstract

Numerical modeling of seismic waves in heterogeneous, porous reservoir rocks is an important tool for interpreting seismic surveys in reservoir engineering. Various theoretical studies derive effective elastic moduli and seismic attributes from complex rock properties, involving patchy saturation and fractured media. To confirm and further develop rock-physics theories for reservoir rocks, accurate numerical modeling tools are required. Our 2D velocity-stress, finite-difference scheme simulates waves within poroelastic media as described by Biot’s theory. The scheme is second order in time, contains high-order spatial derivative operators, and is parallelized using the domain-decomposition technique. A series of numerical experiments that are compared to exact analytical solutions allow us to assess the stability conditions and dispersion relations of the explicit poroelastic finite-differ-ence method. The focus of the experiments is to model wave-induced flow accurately in the vicinity of mesoscopic heterogeneities such as cracks and gas inclusions in partially saturated rocks. For that purpose, a suitable numerical setup is applied to extract seismic attenuation and dispersion from quasi-static experiments. Our results confirm that finite-difference modeling is a valuable tool to simulate wave propa-gation in heterogeneous poroelastic media, provided the temporal and spatial scales of the propagating waves and of the induced fluid-diffusion processes are resolved properly.

Publisher

Society of Exploration Geophysicists

Subject

Geochemistry and Petrology,Geophysics

Reference44 articles.

1. Aldridge, D. F. , N. P. Symons, and L. C. Bartel, 2005, Poroelastic wave propagation with a velocity-stress-pressure algorithm: Proceedings of the 3rd Biot Conference on Poromechanics, 253–258.

2. Numerical simulation of the Biot slow wave in water‐saturated Nivelsteiner Sandstone

3. Seismic waves in rocks with fluids and fractures

4. Theory of Propagation of Elastic Waves in a Fluid‐Saturated Porous Solid. I. Low‐Frequency Range

5. Mechanics of Deformation and Acoustic Propagation in Porous Media

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