Linear viscoelastic behavior of porous media with non-uniform saturation

Heterogeneous moisture distribution is usually observed in partially saturated porous media in the form of saturation patches. Such local heterogeneity can significantly influence the macroscopic hydro-mechanical and acoustic behavior of porous media. In this paper, a linear viscoporoelastic model is presented that can be used to address the effects of local fluid flow in the heterogeneously saturated porous media subjected to a small perturbation. The effects of local flow are characterized using the notion of capillary relaxation. The complex, frequency-dependent material properties characterizing the viscoporoelastic behavior are derived. A rigorous procedure is presented to evaluate the material parameters. The proposed model describes well the effects of patchy saturation on the dispersion and attenuation of the compressional wave in partially saturated rocks. It is found that at high saturation the effects of local gas-pressure redistribution are not negligible. A procedure is proposed to determine the capillary relaxation times using acoustic data. The proposed model provides an alternative methodology to characterize the effects of patchy saturation on the acoustic behavior of partially saturated porous media.