It becomes increasingly clear that non-uniform distribution of immiscible fluids in porous rock is particularly relevant to seismic wave dispersion.White proposed a patchy saturation model in 1975, in which spherical gas pockets were located at the center of a liquid saturated cube.For an extremely light and compressible inner gas,the physical properties can be approximated by a vacuum with White's model.The model successfully analyzes the dispersion phenomena of a P-wave velocity in gas-watersaturated rocks.In the case of liquid pocket saturation, e.g., an oil-pocket surrounded by a water saturated host matrix, the light fluid-pocket assumption is doubtful, and few works have been reported in White's framework.In this work, Poisson's ratio, the bulk modulus, and the effective density of a dual-liquid saturated medium are formulated for the heterogeneous porous rocks containing liquid-pockets.The analysis of the difference between the newly derived bulk modulus and that of White's model shows that the effects of liquid-pocket saturation do not disappear unless the porosity approaches zero.The inner pocket fluid can no longer be ignored.The improvements of the P-wave velocity predictions are illustrated with two examples taken from experiments, i.e., the P-wave velocity in the sandstone saturated by oil and brine and the P-wave velocity for heavy oils and stones at different temperatures.
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