Numerical simulation of ultrasonic waves in reservoir rocks with patchy saturation and fractal petrophysical properties

Abstract

We simulate the propagation of ultrasonic waves in heterogeneous poroviscoelastic media saturated by immiscible fluids. Our model takes into account capillary forces and viscous and mass coupling effects between the fluid phases under variable saturation and pore fluid pressure. The numerical problem is solved in the space-frequency domain using a finite element procedure and the time-domain solution is obtained by a numerical Fourier transform. Heterogeneities due to fluid distribution and rock porosity-permeability are modeled as stochastic fractals, whose spectral densities reproduce saturation an petrophysical variations similar to those observed in reservoir rocks. The numerical experiments are performed at a central frequency of 500 kHz, and show clearly the effects of the different heterogeneities on the amplitudes of shear and compressional waves and the importance of wave mode conversions at the different interfaces.

Finite element modeling of SHTE and PSVTM electroseismics

“…(17)-(20) is also built by means of an iterative hybridized domain decomposed finite element procedure which essentially follows the same ideas as the above described algorithm; different versions of this method have been previously employed to simulate wave propagation in saturated porous media with composite matrices (Santos et al, 2004a,b) and propagation of ultrasonic waves in media with patchy saturation (Santos et al, 2005). Again, here a brief description of the method is given; for details the reader is encouraged to read these last references.…”

“…Notice that in each domain of the finite element partition there exist twelve unknowns, four for each solid displacement component, and two for each component of the fluid displacement. The hybridization implies also here the introduction of Lagrange multipliers, this time associated to generalized forces on the inter-element boundaries Γ jk (Santos et al, 2005).…”

Effect of soil texture on the propagation and attenuation of acoustic wave at unsaturated conditions

“…Parallel to theoretical modeling, numerous numerical investigations have been performed to study the dependence of elastic wave characteristics on water saturation with excitation frequency for consolidated rocks (White, 1975;Murphy, 1982;Tuncay and Corapcioglu, 1996;Helle et al, 2003;Santos et al, 2005), but few ones based on a physically-based theory were conducted for unconsolidated soils. In addition, little is known about the influence of soil texture on acoustic wave motions at unsaturated conditions.…”

The effects of ultrasonics in fragmentation of saturated porous rock samples

“…It has been shown that seismic waves passing through oil saturated rock can generate ultrasonic wave fields [3] as a result of viscoelastic oscillation of the reservoir fluid, dry friction at contacts, bimodal wave vibrations and resonance of gas bubbles in the rock [4,5]. There are also various developing down-hole technologies that involve the direct application of a strong ultrasonic wave field which have shown promising results in enhancing oil recovery due to direct mechanical agitation [6].…”