Rock anelasticity due to patchy saturation and fabric heterogeneity: A double double‐porosity model of wave propagation

Abstract

Heterogeneity of rock's fabric can induce heterogeneous distribution of immiscible fluids in natural reservoirs, since the lithological variations (mainly permeability) may affect fluid migration in geological time scales, resulting in patchy saturation of fluids. Therefore, fabric and saturation inhomogeneities both affect wave propagation. To model the wave effects (attenuation and velocity dispersion), we introduce a double double‐porosity model, where pores saturated with two different fluids overlap with pores having dissimilar compressibilities. The governing equations are derived by using Hamilton's principle based on the potential energy, kinetic energy, and dissipation functions, and the stiffness coefficients are determined by gedanken experiments, yielding one fast P wave and four slow Biot waves. Three examples are given, namely, muddy siltstones, clean dolomites, and tight sandstones, where fabric heterogeneities at three different spatial scales are analyzed in comparison with experimental data. In muddy siltstones, where intrapore clay and intergranular pores constitute a submicroscopic double‐porosity structure, wave anelasticity mainly occurs in the frequency range (104–107 Hz), while in pure dolomites with microscopic heterogeneity of grain contacts and tight sandstones with mesoscopic heterogeneity of less consolidated sands, it occurs at 103–107 Hz and 101–103 Hz (seismic band), respectively. The predicted maximum quality factor of the fast compressional wave for the sandstone is the lowest (approximately 8), and that of the dolomite is the highest. The results of the diffusive slow waves are affected by the strong friction effects between solids and fluids. The model describes wave propagation in patchy‐saturated rocks with fabric heterogeneity at different scales, and the relevant theoretical predictions agree well with the experimental data in fully and partially saturated rocks.

Analysis of attenuation and dispersion of propagating wave due to the coexistence of three fluid phases in the pore volume

“…; Ba et al . ). Nonetheless, it is possible to further improve the efficiency by considering the saturated rock near to actual subsurface situation.…”

“…Even though the theories regarding the estimation of wave propagation through saturated porous media has been improved in recent years, most improvements have been achieved by incorporating various scale mechanisms regarding WIFF in saturated porous rock (Tang 2011;Milani et al 2015;Ba et al 2017). Nonetheless, it is possible to further improve the efficiency by considering the saturated rock near to actual subsurface situation.…”

Effects of Coupling Between Wave‐Induced Fluid Flow and Elastic Scattering on P‐Wave Dispersion and Attenuation in Rocks With Aligned Fractures

“…Instead of specifying the shapes of the background pores, the second type of models describe the background properties using the macroscopic parameters (such as porosity and permeability). This allows us to employ the Biot‐Gassmann theory to study the FB‐WIFF mechanism, for which quite a few models have been developed (e.g., Ba et al, , , ; Brajanovski et al, ; Fu et al, ; Galvin & Gurevich, ; Guo et al, , ; Gurevich et al, ; Kong et al, ). The effects of FB‐WIFF on the P ‐wave dispersion and attenuation are studied in detail using these models.…”

Analytical seismic wave attenuation and velocity dispersion in layered double-porosity media

“…Ba et al [2016] proposed a new doubleporosity model to explain strong velocity dispersion in tight siltstone with clay-filled pores obtained from the experiment. To study the effects of fabric and saturation inhomogeneities on wave attenuation and velocity dispersion, Ba et al [2017] proposed a double double-porosity model and derived the governing equations for this model based on Hamilton's principle. There are one fast P wave and four slow Biot waves in the media when the compressional waves propagate in the double double-porosity model.…”