The Journal of the Acoustical Society of America · 2001 · 398 citations · 34 references
EngineeringEarth SciencesPhysicsAcousticsRock MechanicsSubsurface Fluid FlowFluid SaturationPhysical AcousticsPoromechanics Of RocksRock PhysicsRock PropertiesRock-fluid InteractionsAcoustic Properties Of FluidsBulk ModulusDynamic ModulusFlow Through Porous RockFrequency-domain AcousticsGassmann's EquationPorous MediaSpecific Surface Area
The theory describes the crossover from the Biot–Gassmann–Woods result at low frequencies to the Biot–Gassmann–Hill result at high. The study develops a theory of the dynamic bulk modulus for patchy‑saturated porous rocks within quasi‑static Biot theory, aiming to enable deduction of patch sizes and shapes or accurate sonic‑to‑seismic conversion when saturation values are known. The authors derive exact low‑ and high‑frequency limits and present a simple closed‑form analytic model that incorporates the usual Biot parameters plus two geometrical parameters—specific surface area of the patches and, when one fluid is gas, a simple measure of the stiff fluid patch size. Comparison with exact solutions in simple geometries shows the analytic theory is extremely accurate across the entire frequency range, and the theory, together with experiments, can be used to infer patch sizes and shapes or perform accurate sonic‑to‑seismic conversion when saturation values are known.
The theory of the dynamic bulk modulus, K̃(ω), of a porous rock, whose saturation occurs in patches of 100% saturation each of two different fluids, is developed within the context of the quasi-static Biot theory. The theory describes the crossover from the Biot–Gassmann–Woods result at low frequencies to the Biot–Gassmann–Hill result at high. Exact results for the approach to the low and the high frequency limits are derived. A simple closed-form analytic model based on these exact results, as well as on the properties of K̃(ω) extended to the complex ω-plane, is presented. Comparison against the exact solution in simple geometries for the case of a gas and water saturated rock demonstrates that the analytic theory is extremely accurate over the entire frequency range. Aside from the usual parameters of the Biot theory, the model has two geometrical parameters, one of which is the specific surface area, S/V, of the patches. In the special case that one of the fluids is a gas, the second parameter is a different, but also simple, measure of the patch size of the stiff fluid. The theory, in conjunction with relevant experiments, would allow one to deduce information about the sizes and shapes of the patches or, conversely, to make an accurate sonic-to-seismic conversion if the size and saturation values are approximately known.
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