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A double double-porosity model for wave propagation in patchy-saturated tight sandstone with fabric heterogeneity

In natural reservoir rocks, fabric heterogeneity can further induce heterogeneous geometrical distribution of immiscible multi-phase fluid mixture, since fluid migration may be affected by lithological variation (mainly permeability) in geological time scales, causing patchy saturation of fluids. Both structure heterogeneity and patchy-saturation can lead to strong seismic wave dispersion and attenuation. In this work, a double double-porosity model is presented to describe the overlapping effect of the two heterogeneities on wave dispersion and attenuation. The wave propagation equations are derived from the Hamilton’s principle, and the numerical results for a tight sandstone are compared with corresponding low-frequency experimental data, which shows good agreements. This new model allows for a comprehensive description of wave propagation process in highly complex reservoirs.