Seismic signature of a permeable, dual-porosity layer

Of the key reservoir properties, permeability seems to be the most elusive. Since the middle of the 90s, various seismic attributes have been proposed to map permeability by using detailed analysis of the frequency content of reflected wavetrains. Some attributes are expected to show a relative increase of high-frequency content with increased permeability; other attributes assume the opposite. Actually, both these trends were observed. A possible explanation of these observations is here derived from an effective model of a permeable dual-porosity layer enclosed by impermeable rocks. For such a model, the reflected wavetrain can be regarded as a sum of three components, one of which is related to acousticimpedance contrasts, another to extra compliance caused by P-wave-induced fluid flows between fractures and intergranular pores with a high aspect ratio, and a third to the fluid-flow-induced, inelastic attenuation. In layered reservoirs, all the components tend to be frequency dependent, and the well-known dependence of the first component on the reflecting-layer thickness may strongly dominate the effects of permeability. Hence, predicting the behavior of a permeability attribute in a particular environment requires a modeling formalism that can be called permeability substitution by analogy with the widely used fluid-substitution technique.