Abstract
Hydrocarbon reservoirs usually contain pores and various cracks, which may contain a small amount of bubble fluid. In this study, based on the wave theory of basic porous medium, the influence of various factors on fluid pressure are investigated, and then the stress-strain relationship and Lagrange’s equations with a dissipation function is utilized to derive the elastic wave equation of porous medium containing various cracks and a small amount of bubbly fluid initially. This elastic wave equation describes the influence of squirt flow induced by various cracks on seismic wave attenuation and dispersion, and the influence of the bubble linear vibration on seismic wave attenuation and dispersion effectively. Then, the seismic wave attenuation and dispersion of a given model is estimated and the matching of rock physics parameters are obtained in different frequency bands. The numerical results illustrate that the proposed approach is compatible with previous theory to explain the mechanics of the seismic wave attenuation and dispersion induced by fluid flow and can better describe the propagation of elastic waves in actual rock medium especially for the mechanics of the seismic wave attenuation and dispersion induced by fluid flow within various cracks and a small amount of bubble fluid.
Highlights
Seismic waves in the Earth’s medium possess attenuation and dispersion characteristic over a wide frequency range [Aki and Richards, 1980]
Exploration geophysicists are interested in the inelastic attenuation and dispersion due to the presence of fluid in the pores of the rock [Kumar et al, 2019] by the mechanism wave-induced fluid flow (WIFF) [Müller et al, 2010] including macroscopic scale, microscopic scale and mesoscopic scale
In complex underground porous medium, there may be cases where a small amount of bubble fluid is present in mixed cracks, which means the bubble fluid and various cracks are introduced into the porous rock simultaneously
Summary
Seismic waves in the Earth’s medium possess attenuation and dispersion characteristic over a wide frequency range [Aki and Richards, 1980]. Viscous-inertial attenuation and dispersion due to macroscopic flow is proposed by Biot’s theory [Biot, 1956a, 1956b, 1962; Wang et al, 1990; Pride, 2005; Mavko et al, 2009]. In accordance with these studies, macroscopic flow attenuation well exceeds the seismic frequency band. Coin-type and pinch-type crack is simultaneously introduced into porous medium to describe seismic wave dispersion and attenuation [Wu et al, 2015]. In this study, we propose a model, a porous medium containing various cracks and a small amount of bubble fluid. This new theory retains the basic characteristics of the previous theory, and greatly improves the ability to predict and simulate the propagation of elastic waves in porous medium
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