Mass transfer between fluids as a mechanism for seismic wave attenuation: Experimental evidence from water-CO₂ saturated sandstones

Seismic waves are typically assumed to propagate fast enough through a porous rock saturated with multiple fluid phases such that the interaction between the fluids can be considered adiabatic, or thermodynamically unrelaxed. However, at low gas saturations and when the gas is present in the form of microscopic bubbles the fluid mixture may in fact be thermodynamically relaxed at seismic frequencies. The effective fluid is then significantly more compressible. A transition from a thermodynamically relaxed to unrelaxed state of the fluids will be accompanied by frequency dependent attenuation of the wave in response to heat and/or mass transfer. We conducted forced oscillation experiments on two partially saturated sandstone samples to measure frequency dependent attenuation and modulus dispersion at seismic frequencies (< 1000 Hz). For CO2 saturations of 0.1-0.2% we observe significant attenuation and dispersion in the bulk and shear modulus, with an attenuation peak at similar to 100 Hz. The bulk modulus was significantly lower than the prediction by Gassmann-Wood fluid substitution, which assumes that the fluids are thermodynamically unrelaxed. Numerical simulations in poroelastic media further indicate that a partially drained boundary condition does not adequately explain the observed attenuation and dispersion, particularly in the shear modulus. Numerical simulations at the microscopic scale support the notion that pore-scale heterogeneities could explain the observed shear attenuation and dispersion, since an external shear deformation can cause local compressions of the pore space. The observed attenuation and dispersion are interpreted to be predominantly due to a transition from a thermodynamically relaxed to unrelaxed state of the saturating fluids.